Appendix A: Harmonic polylogarithms
All our results are presented in terms of HPLs which are generalization of Neilson’s polylogarithms. Here we briefly discuss some important properties of HPLs. For more details one can see [41, 46]. The HPLs are represented by \(H(\overset{\rightarrow }{m}_{\omega };y) \); \(\overset{\rightarrow }{m}_{\omega }\) being a \(\omega \)-dimensional vector which belongs to the set \(\{-1,0,1\}\) through which we define the following rational functions:
$$\begin{aligned} f(1;y) \equiv \frac{1}{1-y}, \quad f(0;y) \equiv \frac{1}{y}, \quad f(-1;y) \equiv \frac{1}{1+y}. \end{aligned}$$
(A.1)
The weight-1 (\(\omega = 1\)) HPLs are then defined as
$$\begin{aligned}&H(1,y) \equiv -\text {ln}(1-y), \qquad H(0,y) \equiv \text {ln}(y), \nonumber \\&\quad H(-1,y) \equiv \text {ln}(1+y). \end{aligned}$$
(A.2)
For \(\omega > 1\) HPLs are defined as
$$\begin{aligned} H(m,\overset{\rightarrow }{m}_{\omega };y) \equiv \int _{0}^{y} ~ \mathrm{d}x ~ f(m,x) ~ H(\overset{\rightarrow }{m}_{\omega };x),\quad m \in 0, \pm {1}. \end{aligned}$$
(A.3)
Moreover, the higher dimensional HPLs are defined following Eq. (A.3) for the new elements 2,3 in \(\overset{\rightarrow }{m}_{\omega }\), representing a new class of rational functions
$$\begin{aligned}&f(2;y) \equiv f(1-z;y) \equiv \frac{1}{1-y-z}, \nonumber \\&f(3;y) \equiv f(z;y) \equiv \frac{1}{y+z}; \end{aligned}$$
(A.4)
correspondingly the weight-1 (\(\omega = 1\)) two-dimensional HPLs are given by
$$\begin{aligned} H(2,y) \equiv -\text {ln}\left( 1-\frac{y}{1-z} \right) , \qquad H(3,y) \equiv \text {ln}\left( \frac{y+z}{z}\right) . \end{aligned}$$
(A.5)
1.1 Properties
HPLs have some important properties:
Shuffle algebra Product of two HPLs with weights \(\omega _1\) and \(\omega _2\) of same argument y is a HPL of weight (\(\omega _1 + \omega _1\)) and argument y. This way all possible permutations of the elements of \(\overset{\rightarrow }{m}_{\omega _1}\) and \(\overset{\rightarrow }{m}_{\omega _2}\) are considered preserving the relative orders of the element of \(\overset{\rightarrow }{m}_{\omega _1}\) and \(\overset{\rightarrow }{m}_{\omega _2}\),
$$\begin{aligned} H(\overset{\rightarrow }{m}_{\omega _1};y)~H(\overset{\rightarrow }{m}_{\omega _2};y) = \sum _{ \overset{\rightarrow }{m}_{\omega } = \overset{\rightarrow }{m}_{\omega _1} \biguplus \overset{\rightarrow }{m}_{\omega _2} } H(\overset{\rightarrow }{m}_{\omega };y) \end{aligned}$$
(A.6)
Integration-by-parts identities Using the integration-by-parts identities the ordering of the elements of \(\overset{\rightarrow }{m}_{\omega }\) inside the HPL can be reversed and in this process some products of two HPLs can be generated.
$$\begin{aligned} H(\overset{\rightarrow }{m}_{\omega };y)&\equiv H(m_{1},m_{2},\ldots m_{\omega }; y) = H(m_{1} ; y)~H(m_{2},\ldots m_{\omega }; y) \nonumber \\&\quad - H(m_{2},m_{1} ; y)~H(m_{3},\ldots m_{\omega }; y)\nonumber \\&\quad + \cdots + (-1)^{\omega + 1}~H(m_{\omega },\ldots , m_{2}, m_{1}; y). \end{aligned}$$
(A.7)
Equations A.6 and A.7 are very useful in writing the higher-weight HPLs in terms of lower-weight HPLs or products of HPLs, which have been used in the checks of the different poles in Sect. 5. Below we provide the necessary relations of HPLs used in our computation.
$$\begin{aligned} H(0,2,0,y)&= H(0,y) H(0,2,y) - 2 H(0,0,2,y),\nonumber \\ H(1,0,2,y)&= H(1,y) H(0,2,y) - H(0,1,2,y) - H(0,2,1,y),\nonumber \\ H(1,2,0,y)&= H(1,y) H(2,0,y) - H(2,1,y) H(0,y) + H(0,2,1,y),\nonumber \\ H(2,0,0,y)&= H(2,y) H(0,0,y) - H(0,2,y) H(0,y) + H(0,0,2,y),\nonumber \\ H(2,0,2,y)&= H(2,y) H(0,2,y) - 2 H(0,2,2,y),\nonumber \\ H(2,2,2,y)&= \frac{1}{3} H(2,y) H(2,2,y),\nonumber \\ H(2,2,0,y)&= H(2,y) H(2,0,y) - H(2,2,y) H(0,y) + H(0,2,2,y),\nonumber \\ H(3,0,2,y)&= H(3,y) H(0,2,y) - H(0,3,2,y) - H(0,2,3,y),\nonumber \\ H(3,2,0,y)&= H(3,y) H(2,0,y) - H(2,3,y) H(0,y) + H(0,2,3,y),\nonumber \\ H(3,3,2,y)&= H(3,y) H(3,2,y) - H(3,3,y) H(2,y) + H(2,3,3,y),\nonumber \\ H(2,1,0,y)&= H(2,y) H(1,0,y) - H(1,2,y) H(0,y) + H(0,1,2,y),\nonumber \\ H(2,3,2,y)&= H(2,y) H(3,2,y) - 2 H(3,2,2,y) \end{aligned}$$
(A.8)
Appendix B: One-loop coefficients
$$\begin{aligned} \mathcal {A}_{0}^{(1)}&= -\frac{\beta _{0}}{2} ~ \mathcal {A}_{0}; \\ \mathcal {A}_{1;C_{A}}^{(1)}&= - {C_A} ~ \mathcal {A}_{0}; \qquad \mathcal {A}_{1;C_{F}}^{(1)} = 0; \qquad \mathcal {A}_{1;n_{f}}^{(1)} = 0;\\ \mathcal {A}_{2;C_{A}}^{(1)}&= \Bigg \{-6 (-1 + y) y^4 (-1 + z) (y + z) + 6 (-1 + y) y^5 (-1 + z) (y + z) + 84 (-1 + y) y^3 (-1 + z) z (y + z) \\&\quad - 54 (-1 + y) y^4 (-1+ z) z (y + z) + 44 (-1 + y) y^5 (-1 + z) z (y + z) + 132 (-1 + y) y^2 (-1 + z) z^2 (y + z) \\&\quad - 152 (-1 + y) y^3 (-1 + z) z^2 (y+ z) + 48 (-1 + y) y^5 (-1 + z) z^2 (y + z) + 84 (-1 + y) y (-1 + z) z^3 (y + z)\\&\quad - 152 (-1 + y) y^2 (-1 + z) z^3 (y + z) - 88 (-1+ y) y^3 (-1 + z) z^3 (y + z) + 144 (-1 + y) y^4 (-1 + z) z^3 (y + z) \\&\quad - 6 (-1 + y) (-1 + z) z^4 (y + z) - 54 (-1 + y) y (-1+ z) z^4 (y + z) + 144 (-1 + y) y^3 (-1 + z) z^4 (y + z) \\&\quad + 6 (-1 + y) (-1 + z) z^5 (y + z) + 44 (-1 + y) y (-1 + z) z^5 (y + z)+ 48 (-1 + y) y^2 (-1 + z) z^5 (y + z)\\&\quad + 3 (-1 + y) y (-1 + z) (y + z)^4 (16 y^3 + y^2 (-41 + 12 z) - 2 (7 - 6 z + 3 z^2)+ 3 y (13 - 9 z + 4 z^2)) H(0, y)^2 \\&\quad + 3 (-1 + y) (-1 + z) z (y + z)^4 (-14 + 39 z - 41 z^2 + 16 z^3 + 6 y^2 (-1 + 2 z) + 3 y (4- 9 z + 4 z^2)) H(0, z)^2 \\&\quad + 3 (-1 + y) (-1 + z) (y + z)^4 (4 + 16 y^4 - 22 z + 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43 + 20 z)+ 3 y^2 (15 - 17 z + 8 z^2) \\&\quad + y (-22 + 48 z - 51 z^2 + 20 z^3)) H(1, z)^2 + 2 (-1 + z) (y + z)^4 H(0, y) (-10 + 30 y - 35 y^2+ 20 y^3 - 5 y^4 + 20 z\\&\quad - 80 y z + 132 y^2 z - 116 y^3 z + 44 y^4 z - 15 z^2 + 60 y z^2 - 72 y^2 z^2 + 24 y^3 z^2 + 5 z^3- 25 y z^3 + 20 y^2 z^3 \\&\quad + 3 (-1 + y) (2 + y^2 (3 - 9 z) - 4 z + 3 z^2 - z^3 + y^3 (-1 + 4 z) + y (-4 + 12 z - 9 z^2+ 4 z^3)) H(0, z) \\&\quad + 3 (-1 + y) (2 + 16 y^4 - 4 z + 3 z^2 - z^3 + 2 y^3 (-21 + 8 z) + 6 y^2 (7 - 6 z + 2 z^2) + y (-18 + 24 z\\&\quad - 15 z^2 + 4 z^3)) H(1, z)) + (-1 + y) (-1 + z) (y^7 (-9 + 84 z) + 3 y^6 (9 - 83 z + 144 z^2) - 9 z^4 (-2 + 4 z - 3 z^2 + z^3)\\&\quad + 3 y^5 (-12 + 92 z - 373 z^2 + 324 z^3) + y z^3 (-36 - 136 z + 276 z^2 - 249 z^3 + 84 z^4) + y^2 z^2 (-60 - 292 z + 1053 z^2\\&\quad - 1119 z^3 + 432 z^4) + y^3 z (-36 - 292 z + 1608 z^2 - 2175 z^3 + 972 z^4) + y^4 (18 - 136 z + 1053 z^2 - 2175 z^3\\&\quad + 1248 z^4)) H(2, y) + 3 (-1 + y) (-1 + z) (y + z)^4 (4 + 16 y^4 - 22 z + 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43 + 20 z) \\&\quad + 3 y^2 (15- 17 z + 8 z^2) + y (-22 + 48 z - 51 z^2 + 20 z^3)) H(2, y)^2 + 2 (-1 + y) (y + z)^4 H(0, z) (-5 (-1 + z)^2 (2\\&\quad - 2 z + z^2)+ 5 y^3 (1 - 5 z + 4 z^2) + 3 y^2 (-5 + 20 z - 24 z^2 + 8 z^3) + 4 y (5 - 20 z + 33 z^2 - 29 z^3 + 11 z^4) \\&\quad + 3 (-1 + z) (y^3 (-1+ 4 z) + 4 y (-1 + z)^2 (-1 + 4 z) + 3 y^2 (1 - 5 z + 4 z^2) + 2 (1 - 9 z + 21 z^2 - 21 z^3 \\&\quad + 8 z^4)) H(2, y))+ (-1 + y) (-1+ z) H(1, z) (3 y^7 (-3 + 28 z) + 3 y^6 (9 - 83 z + 144 z^2) - 9 z^4 (-2 + 4 z - 3 z^2 \\&\quad + z^3)+ 3 y^5 (-12 + 92 z - 373 z^2+ 324 z^3) + y z^3 (-36 - 136 z + 276 z^2 - 249 z^3 + 84 z^4) + y^2 z^2 (-60 - 292 z \\&\quad + 1053 z^2 - 1119 z^3 + 432 z^4)+ y^3 z (-36 - 292 z + 1608 z^2 - 2175 z^3 + 972 z^4) + y^4 (18 - 136 z + 1053 z^2 \\&\quad - 2175 z^3+ 1248 z^4) - 6 (y + z)^4 (4+ 16 y^4 - 22 z + 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z \\&\quad + 8 z^2) + y (-22 + 48 z - 51 z^2+ 20 z^3)) H(3, y)) - 6 (-1 + y) y (-1 + z) (y + z)^4 (16 y^3 + y^2 (-41 + 12 z) \\&\quad - 2 (7 - 6 z + 3 z^2) + 3 y (13 - 9 z+ 4 z^2)) H(0, 0, y) - 6 (-1 + y) (-1 + z) z (y + z)^4 (-14 + 39 z - 41 z^2 + 16 z^3 \\&\quad + 6 y^2 (-1 + 2 z) + 3 y (4 - 9 z+ 4 z^2)) H(0, 0, z) - 6 (-1 + y) (-1 + z) (y + z)^4 (2 + 16 y^4 - 4 z + 3 z^2 - z^3 \\&\quad + 2 y^3 (-21 + 8 z) + 6 y^2 (7 - 6 z+ 2 z^2) + y (-18 + 24 z - 15 z^2 + 4 z^3)) H(0, 1, z) + 6 (-1 + y) (-1 + z) (y \\&\quad + z)^4 (2 + 16 y^4 - 4 z + 3 z^2 - z^3+ 2 y^3 (-21 + 8 z) + 6 y^2 (7 - 6 z + 2 z^2) + y (-18 + 24 z - 15 z^2 \\&\quad + 4 z^3)) H(0, 2, y) - 6 (-1 + y) y (-1 + z) (y+ z)^4 (16 y^3 + y^2 (-41 + 12 z) - 2 (7 - 6 z + 3 z^2) + 3 y (13\\&\quad - 9 z + 4 z^2)) H(1, 0, y) + 6 (-1 + y) (-1 + z) (y + z)^4 (2+ y^2 (3 - 9 z) - 4 z + 3 z^2 \\&\quad - z^3 + y^3 (-1 + 4 z) + y (-4 + 12 z - 9 z^2 + 4 z^3)) H(1, 0, z) - 6 (-1 + y) (-1 + z) (y+ z)^4 (4 + 16 y^4 - 22 z \\&\quad + 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z + 8 z^2) + y (-22 + 48 z - 51 z^2\\ \end{aligned}$$
$$\begin{aligned}&\quad + 20 z^3)) H(1, 1, z) + 6 (-1 + y) (-1 + z) (y + z)^4 (2 + 16 y^4 - 4 z + 3 z^2 - z^3 + 2 y^3 (-21 + 8 z) + 6 y^2 (7 - 6 z\\&\quad + 2 z^2) + y (-18 + 24 z - 15 z^2 + 4 z^3)) H(2, 0, y) - 6 (-1 + y) (-1 + z) (y + z)^4 (4 + 16 y^4 - 22 z + 45 z^2 - 43 z^3\\&\quad + 16 z^4 + y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z + 8 z^2) + y (-22 + 48 z - 51 z^2 + 20 z^3)) H(2, 2, y) - 6 (-1 \\&\quad + y) (-1 + z) (y+ z)^4 (4 + 16 y^4 - 22 z + 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z + 8 z^2) \\&\quad + y (-22 + 48 z - 51 z^2+ 20 z^3)) H(3, 2, y)\Bigg \}\Big / \Big (24 (-1 + y) y (-1 + z) z (-1 + y + z) (y + z)^4\Big );\\ \mathcal {A}_{2;C_{F}}^{(1)}&= \Bigg \{20 (-1 + y) y (-1 + z) (y + z) - 59 (-1 + y) y^2 (-1 + z) (y + z) + 68 (-1 + y) y^3 (-1 + z) (y + z) \\&\quad - 39 (-1 + y) y^4 (-1+ z) (y + z) + 10 (-1 + y) y^5 (-1 + z) (y + z) + 20 (-1 + y) (-1 + z) z (y + z) - 138 (-1 \\&\quad + y) y (-1 + z) z (y + z) + 316 (-1+ y) y^2 (-1 + z) z (y + z) - 318 (-1 + y) y^3 (-1 + z) z (y + z) + 161 (-1 \\&\quad + y) y^4 (-1+ z) z (y + z) - 41 (-1 + y) y^5 (-1+ z) z (y + z) - 59 (-1 + y) (-1 + z) z^2 (y + z) + 316 (-1\\&\quad + y) y (-1 + z) z^2 (y + z) - 578 (-1 + y) y^2 (-1 + z) z^2 (y + z)+ 435 (-1 + y) y^3 (-1 + z) z^2 (y + z) - 142 (-1 \\&\quad + y) y^4 (-1 + z) z^2 (y + z) + 28 (-1+ y) y^5 (-1 + z) z^2 (y + z) + 68 (-1+ y) (-1 + z) z^3 (y + z) - 318 (-1 \\&\quad + y) y (-1+ z) z^3 (y + z) + 435 (-1 + y) y^2 (-1 + z) z^3 (y + z) - 202 (-1 + y) y^3 (-1\\ \end{aligned}$$
$$\begin{aligned}&\quad + z) z^3 (y + z) + 20 (-1 + y) y^4 (-1 + z) z^3 (y + z) - 39 (-1 + y) (-1 + z) z^4 (y + z) + 161 (-1 + y) y (-1 \\&\quad + z) z^4 (y + z)- 142 (-1 + y) y^2 (-1 + z) z^4 (y + z) + 20 (-1 + y) y^3 (-1 + z) z^4 (y + z) + 10 (-1 + y) (-1 \\&\quad + z) z^5 (y + z) - 41 (-1+ y) y (-1 + z) z^5 (y + z) + 28 (-1 + y) y^2 (-1 + z) z^5 (y + z) - (-1 + y)^2 (-1 \\&\quad + 4 y) (-1 + z)^2 (y+ z)^2 (-2 + 2 y^3 + 4 z- 3 z^2 + z^3 + y^2 (-6 + 4 z) + y (6 - 8 z + 3 z^2)) H(0, y)^2 + (1 \\&\quad - y) (-1 + y) (y^3+ 3 y^2 (-1 + z)+ 4 y (-1 + z)^2 + 2 (-1+ z)^3) (-1 + z)^2 (y + z)^2 (-1 + 4 z) H(0, z)^2 \\&\quad + (1 - y) (-1 + y) (-1 + z)^2 (y + z)^2 (4+ 8 y^4 - 18 z + 33 z^2 - 27 z^3+ 8 z^4 + y^3 (-27 + 20 z) + 3 y^2 (11 \\&\quad - 17 z + 8 z^2) + y (-18 + 48 z - 51 z^2 + 20 z^3)) H(1, z)^2+ (-1 + z)^2 (-1 + y + z) (y+ z)^2 H(0, y) (-(y z (8 y^3 \\&\quad + y (30 - 27 z) + 12 (-1 + z) + 2 y^2 (-13 + 6 z))) - 2 (-1 + y)^2 (-1+ 4 y) (2 + 2 y^2 + 2 y (-2+ z) - 2 z \\&\quad + z^2) H(1, z)) + (1 - y) (-1 + y) (-1 + z)^2 (y^5 (-3 + 20 z) + y^4 (9 - 73 z+ 80 z^2) - 3 z^2 (-2 + 4 z - 3 z^2+ z^3) \\&\quad + 6 y^3 (-2 + 15 z - 34 z^2 + 20 z^3) + y z (-8 - 32 z+ 90 z^2 - 73 z^3 + 20 z^4) + 2 y^2 (3 - 16 z + 81 z^2 - 102 z^3 \\&\quad + 40 z^4)) H(2, y) + (1 - y) (-1 + y) (-1 + z)^2 (y + z)^2 (4 + 8 y^4 - 18 z+ 33 z^2 - 27 z^3 + 8 z^4 + y^3 (-27 + 20 z)\\&\quad + 3 y^2 (11 - 17 z + 8 z^2) + y (-18 + 48 z - 51 z^2 + 20 z^3)) H(2, y)^2 + (1 - y) (-1 + y) (-1 + y + z) (y\\&\quad + z)^2 H(0, z) (y z (-12+ 30 z - 26 z^2 + 8 z^3 + 3 y (4 - 9 z + 4 z^2)) + 2 (y^2 + 2 y (-1 + z) + 2 (-1 + z)^2) (-1 \\&\quad + z)^2 (-1+ 4 z) H(2, y)) + (-1 + y + z) (-1 + y + z - y z)^2 H(1, z) (y^4 (3 - 20 z) + y^3 (-6 + 50 z - 60 z^2) \\&\quad + 3 z^2 (2 - 2 z+ z^2)+ y^2 (6 - 34 z + 94 z^2 - 60 z^3) - 2 y z (4 + 17 z - 25 z^2 + 10 z^3) + 2 (y + z)^2 (-4 + 8 y^3 \\&\quad + 14 z - 19 z^2 + 8 z^3+ y^2 (-19 + 12 z) + 2 y (7 - 10 z + 6 z^2)) H(3, y)) + 2 (1 - y) (1 - 5 y + 4 y^2) (-y \\&\quad - z) (-1 + z)^2 (2 y^4 + 6 y^3 (-1 + z)+ y^2 (6 - 14 z + 7 z^2) + z (-2 + 4 z - 3 z^2 + z^3) + y (-2 + 10 z \\&\quad - 11 z^2 + 4 z^3)) H(0, 0, y) + 2 (1 - y) (-1 + y) (-y- z) (-1 + z) (1 - 5 z + 4 z^2) (y^4 + 2 (-1 + z)^3 z \\&\quad + 2 y (-1 + z)^2 (-1 + 3 z)+ y^3 (-3 + 4 z) + y^2 (4 - 11 z+ 7 z^2)) H(0, 0, z)\\&\quad + 2 (-1 + y)^2 (-1 + 4 y) (-1 + z)^2 (y + z)^2 (-2+ 2 y^3 + 4 z - 3 z^2 + z^3 + y^2 (-6 + 4 z)\\&\quad + y (6 - 8 z+ 3 z^2)) H(0, 1, z) - 2 (-1 + y)^2 (-1 + 4 y) (-1 + z)^2 (y + z)^2 (-2 \\&\quad + 2 y^3 + 4 z - 3 z^2 + z^3 + y^2 (-6 + 4 z) + y (6 - 8 z+ 3 z^2)) H(0, 2, y)+ 2 (-1 + y)^2 (-1\\&\quad + 4 y) (-1 + z)^2 (y + z)^2 (-2 + 2 y^3 + 4 z - 3 z^2 + z^3 + y^2 (-6 + 4 z) + y (6 - 8 z+ 3 z^2)) H(1, 0, y)\\&\quad + 2 (-1 + y)^2 (-1 + z)^2 (y + z)^2 (4 + 8 y^4 - 18 z + 33 z^2 - 27 z^3 + 8 z^4 + y^3 (-27 + 20 z)+ 3 y^2 (11 - 17 z + 8 z^2)\\&\quad + y (-18 + 48 z - 51 z^2 + 20 z^3)) H(1, 1, z) - 2 (-1 + y)^2 (-1 + 4 y) (-1 + z)^2 (y + z)^2 (-2\\&\quad + 2 y^3 + 4 z - 3 z^2 + z^3 + y^2 (-6 + 4 z) + y (6 - 8 z + 3 z^2)) H(2, 0, y) + 2 (-1 + y)^2 (-1 + z)^2 (y + z)^2 (4 + 8 y^4\\&\quad - 18 z + 33 z^2 - 27 z^3 + 8 z^4 + y^3 (-27 + 20 z) + 3 y^2 (11 - 17 z + 8 z^2) + y (-18 + 48 z - 51 z^2 + 20 z^3)) H(2, 2, y)\\&\quad + 2 (-1 + y)^2 (-1 + z)^2 (y + z)^2 (4 + 8 y^4 - 18 z + 33 z^2 - 27 z^3 + 8 z^4 + y^3 (-27 + 20 z) + 3 y^2 (11 - 17 z + 8 z^2)\\&\quad + y (-18 + 48 z - 51 z^2 + 20 z^3)) H(3, 2, y)\Bigg \}\Big / \Big (4 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2\Big );\\ \mathcal {A}_{2;n_{f}}^{(1)}&= \Bigg \{-24 y^4 z + 12 y^5 z - 8 y^6 z - 24 y^3 z^2 + 8 y^4 z^2 - 8 y^5 z^2 - 24 y^2 z^3 - 8 y^3 z^3 + 16 y^4 z^3 - 24 y z^4\\&\quad + 8 y^2 z^4 + 16 y^3 z^4 + 12 y z^5 - 8 y^2 z^5 - 8 y z^6 - (y + z)^4 (2 + y^2 (3 - 9 z) - 4 z + 3 z^2 - z^3 + y^3 (-1 + 4 z)\\&\quad + y (-4 + 12 z - 9 z^2 + 4 z^3)) H(0, y) - (y + z)^4 (2 + y^2 (3 - 9 z) - 4 z + 3 z^2 - z^3 + y^3 (-1 + 4 z) + y (-4 + 12 z\\&\quad - 9 z^2 + 4 z^3)) H(0, z) + 4 y z (-5 y^3 + 3 y^4 + y z^2 + y^2 (6 + z - 6 z^2) + z^2 (6 - 5 z + 3 z^2)) H(1, z) + 4 y z (-5 y^3\\&\quad + 3 y^4 + y z^2 + y^2 (6 + z - 6 z^2) + z^2 (6 - 5 z + 3 z^2)) H(2, y)\Bigg \}\Big /\Big (24 y z (-1 + y + z) (y + z)^4\Big ).\\ \end{aligned}$$
Appendix C: Two-loop coefficients
$$\begin{aligned} \mathcal {A}_{0}^{(2)}&= -\frac{3 \beta _{0}^{2}}{8} ~ \mathcal {A}_{0}; \\ \mathcal {A}_{1;C_{A}^{2}}^{(2)}&= - ~ \mathcal {A}_{0}; \qquad \mathcal {A}_{1;C_{F}^{2}}^{(2)} = 24 ~ \mathcal {A}_{0}; \qquad \mathcal {A}_{1;n_{f}^{2}}^{(2)} = 0; \qquad \mathcal {A}_{1;C_{A}C_{F}}^{(2)} = - 26 ~ \mathcal {A}_{0}; \qquad \mathcal {A}_{1;C_{A}n_{f}}^{(2)} = 0; \qquad \mathcal {A}_{1;C_{F}n_{f}}^{(2)} = 0; \\ \mathcal {A}_{2;C_{A}^{2}}^{(2)}&= \frac{55}{12}~ \mathcal {A}_{0}; \qquad \mathcal {A}_{2;C_{F}^{2}}^{(2)} {=} -12 ~ \mathcal {A}_{0}; \qquad \mathcal {A}_{2;n_{f}^{2}}^{(2)} {=} 0; \qquad \mathcal {A}_{2;C_{A}C_{F}}^{(2)} {=} \frac{23}{2} ~ \mathcal {A}_{0}; \qquad \mathcal {A}_{2;C_{A}n_{f}}^{(2)} {=} -\frac{5}{6} \mathcal {A}_{0}; \qquad \mathcal {A}_{2;C_{F}n_{f}}^{(2)} = - ~ \mathcal {A}_{0};\\ \mathcal {A}_{3;C_{A}^{2}}^{(2)}&= \Bigg \{8 (-1 + y)^2 y (-1 + z)^2 z (y + z) (39 y^6 (-1 + 4 z) + y^5 (84 - 710 z + 204 z^2) + 3 z^3 (26 - 41 z + 28 z^2 - 13 z^3)\\&\quad - 3 y^4 (41 - 372 z + 507 z^2 + 56 z^3) + 2 y z^2 (117 - 543 z + 558 z^2 - 355 z^3 + 78 z^4) - 2 y^3 (-39 + 543 z - 1354 z^2\\&\quad + 850 z^3 + 84 z^4) + y^2 z (234 - 1662 z + 2708 z^2 - 1521 z^3 + 204 z^4)) - 8 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (56 \\&\quad + 500 y^4+ 34 z - 396 z^2 + 550 z^3 - 244 z^4 + y^3 (-1415 + 1348 z) + 3 y^2 (433 - 715 z + 180 z^2) - 4 y (110 \\&\quad - 219 z + 42 z^2+ 38 z^3)) H(0, y)^3 + 8 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (-56 + 244 y^4 + 440 z - 1299 z^2 \\&\quad + 1415 z^3 - 500 z^4+ 2 y^3 (-275+ 76 z) + y^2 (396 + 168 z - 540 z^2) - y (34 + 876 z - 2145 z^2 \\&\quad + 1348 z^3)) H(0, z)^3 - 32 (-1 + y)^2 y (-1+ z)^2 z (y + z)^4 (9+ 364 y^4 - 203 z + 702 z^2 - 872 z^3 + 364 z^4\\&\quad + y^3 (-872 + 564 z) + 6 y^2 (117 - 167 z + 92 z^2) + y (-203 + 606 z - 1002 z^2+ 564 z^3)) H(1, z)^3 \\&\quad + (-1728 y^{12} (-1 + z)^2+ 216 (-1 + z)^5 z^6 (-1 + 4 z) + 24 y^{11} (-1 + z)^2 (375 + 718 z) + y^{10} (-19080\\&\quad - 28289 z + 250122 z^2 - 338949 z^3 + 136304 z^4) - y (-1 + z)^2 z^5 (-8082 + 36428 z - 80967 z^2 + 91745 z^3\\&\quad - 40992 z^4 + 1728 z^5)+ y^9 (20808 + 63133 z - 748547 z^2 + 1624467 z^3 - 1359901 z^4\\&\quad + 400256 z^5) + y^2 (-1 + z)^2 z^4 (25944 - 171016 z + 438304 z^2- 585767 z^3 + 364650 z^4 - 73560 z^5 + 864 z^6)\\&\quad + y^8 (-12024 - 69787 z + 1130000 z^2 - 3636494 z^3 + 4922656 z^4 - 3035579 z^5+ 701120 z^6) + y^7 (3312\\&\quad + 52501 z - 1005911 z^2 + 4577790 z^3 - 9135618 z^4 + 9138769 z^5 - 4491307 z^6 + 860032 z^7)+ y^3 z^3 (32844 \\&\quad - 401168 z + 1810731 z^2 - 4338377 z^3 + 6108582 z^4 - 5103134 z^5 + 2392815 z^6 - 537669 z^7 + 35376 z^8)\\&\quad + y^4 z^2 (23424- 374888 z + 2225864 z^2 - 6614805 z^3 + 11116384 z^4 - 10963698 z^5 + 6184528 z^6 - 1787581 z^7 \\&\quad + 190880 z^8)+ y^5 z (6066 - 175600 z + 1559775 z^2 - 6176973 z^3 + 12917254 z^4 - 15269476 z^5 + 10196989 z^6\\&\quad - 3546779 z^7 + 488960 z^8)+ y^6 (-288 - 26312 z + 553704 z^2 - 3461777 z^3 + 9763000 z^4-14401588 z^5\\&\quad + 11527644 z^6- 4728907 z^7 + 774416 z^8)) H(2, y)^2 - 32 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (9 + 364 y^4\\&\quad - 203 z +702 z^2 - 872 z^3 + 364 z^4 + y^3 (-872 + 564 z) + 6 y^2 (117 - 167 z+ 92 z^2) + y (-203 + 606 z\\&\quad - 1002 z^2 + 564 z^3)) H(2, y)^3 + H(0, y)^2 ((y + z)^2 (1728 y^{10} (-1 + z)^2 + 216 (-1 + z)^5 z^3 (-1\\&\quad + 4 z) - 72 y^9 (-1 + z)^2 (149 + 87 z) + y^8 (28080 - 43945 z - 17990 z^2 + 55603 z^3 - 21640 z^4)\\&\quad + y (-1 + z)^2 z^2 (144 - 3573 z+ 10219 z^2 - 12168 z^3 + 4234 z^4+ 864 z^5) - y^7 (39888 - 94511 z \\&\quad + 2851 z^2 + 137595 z^3 - 104887 z^4 + 19064 z^5) + y^6 (32832- 125478 z + 90408 z^2+ 113163 z^3 - 158918 z^4\\&\quad + 46681 z^5 + 1096 z^6) - y^2 (-1 + z)^2 z (360 - 2430 z - 10125 z^2 + 18134 z^3- 1460 z^4 - 13140 z^5 + 4320 z^6) \\&\quad + y^5 (-15336+ 94486 z - 141904 z^2 + 19649 z^3 + 66045 z^4 + 13557 z^5 - 53601 z^6 + 17104 z^7)+ y^4 (3600\\&\quad - 38177 z + 94480 z^2 - 70947 z^3 + 25180 z^4 - 94718 z^5 + 142546 z^6 - 75040 z^7 + 13184 z^8) + y^3 (-288 \\&\quad + 7227 z- 28965 z^2 + 25131 z^3 + 4151 z^4 + 35390 z^5 - 108748 z^6 + 97128 z^7 - 33618 z^8 + 2592 z^9))\\&\quad + 48 (-1 + y)^2 y (-1 + z)^2 z (y+ z)^4 (16 y^4 + 4 y^3 (-11 + 6 z) + 6 y^2 (8 - 9 z + 2 z^2) \\&\quad - 3 (-2 + 4 z - 3 z^2 + z^3) + y (-26 + 48 z - 33 z^2 + 12 z^3)) H(0, z)+ 144 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (2\\&\quad + 16 y^4 - 4 z + 3 z^2 - z^3 + 2 y^3 (-21 + 8 z) + 6 y^2 (7 - 6 z + 2 z^2) + y (-18+ 24 z - 15 z^2 + 4 z^3)) H(1, z)\\&\quad + 48 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (2 + 16 y^4 - 4 z + 3 z^2 - z^3 + 2 y^3 (-21 + 8 z)+ 6 y^2 (7 - 6 z + 2 z^2) \\&\quad + y (-18+ 24 z - 15 z^2 + 4 z^3)) H(2, y)) + H(0, z)^2 ((y + z)^2 (1728 y^9 (-1 + z)^2 (-1 + 3 z)- 216 (-1 \\&\quad + z)^6 z^3 (-1 + 4 z)+ y^8 (9000 - 48470 z + 93492 z^2 - 78258 z^3 + 23552 z^4) + 4 y^7 (-4770 + 28897 z - 69529 z^2 \end{aligned}$$
$$\begin{aligned}&+ 79974 z^3 - 42772 z^4 + 8200 z^5) + y (-1 + z)^2 z^2 (144 - 3501 z + 19081 z^2 - 43239 z^3 + 50375 z^4 \\&- 23976 z^5 + 1728 z^6)+ y^6 (20808 - 148735 z + 427794 z^2 - 614728 z^3 + 447358 z^4 - 140145 z^5 + 9016 z^6) \\&+ y^5 (-12024 + 107821 z - 367983 z^2+ 619778 z^3 - 507386 z^4 + 132177 z^5 + 54601 z^6 - 26984 z^7) \\&- y^2 (-1 + z)^2 z (360 - 2934 z- 12651 z^2 + 74708 z^3 - 142537 z^4+ 119942 z^5 - 36936 z^6 + 864 z^7) \\&+ y^4 (3312 - 41639 z + 174106 z^2 - 315241 z^3+ 188404 z^4 + 184665 z^5 - 356162 z^6+ 199207 z^7 - 37336 z^8)\\&+ y^3 (-288 + 7155 z - 40995 z^2 + 60519 z^3 + 92277 z^4 - 437623 z^5 + 633399 z^6 - 444135 z^7 + 146323 z^8\\&- 16632 z^9)) + 48 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (y^3 (-1 + 4 z) + 4 y (-1 + z)^2 (-1 + 4 z) + 3 y^2 (1 - 5 z + 4 z^2)\\&+ 2 (1- 9 z + 21 z^2 - 21 z^3 + 8 z^4)) H(1, z) + 144 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (y^3 (-1 + 4 z)+ 4 y (-1\\&+ z)^2 (-1 + 4 z)+ 3 y^2 (1 - 5 z + 4 z^2)+ 2 (1 - 9 z + 21 z^2 - 21 z^3 + 8 z^4)) H(2, y)) + H(1, z)^2 (-1728 y^{12} (-1 \\&+ z)^2 + 216 (-1+ z)^5 z^6 (-1 + 4 z) + 24 y^{11} (-1 + z)^2 (375 + 718 z) + y^{10} (-19080 - 28289 z + 250122 z^2\\&- 338949 z^3 + 136304 z^4) -y (-1+ z)^2 z^5 (-8082 + 36428 z - 80967 z^2 + 91745 z^3 - 40992 z^4 + 1728 z^5) \\&+ y^9 (20808 + 63133 z - 748547 z^2 + 1624467 z^3- 1359901 z^4 + 400256 z^5) + y^2 (-1 + z)^2 z^4 (25944\\&- 171016 z + 438304 z^2 - 585767 z^3 + 364650 z^4 - 73560 z^5 + 864 z^6)+ y^8 (-12024 - 69787 z + 1130000 z^2\\&- 3636494 z^3 + 4922656 z^4 - 3035579 z^5 + 701120 z^6) + y^7 (3312 + 52501 z - 1005911 z^2+ 4577790 z^3 \\&- 9135618 z^4 + 9138769 z^5 - 4491307 z^6 + 860032 z^7) + y^3 z^3 (32844 - 401168 z + 1810731 z^2 - 4338377 z^3 \end{aligned}$$
$$\begin{aligned}&+ 6108582 z^4 - 5103134 z^5 + 2392815 z^6 - 537669 z^7 + 35376 z^8) + y^4 z^2 (23424 - 374888 z + 2225864 z^2 \\&- 6614805 z^3+ 11116384 z^4 - 10963698 z^5 + 6184528 z^6 - 1787581 z^7 + 190880 z^8) + y^5 z (6066 - 175600 z \\&+ 1559775 z^2 - 6176973 z^3+ 12917254 z^4 - 15269476 z^5 + 10196989 z^6 - 3546779 z^7 + 488960 z^8) + y^6 (-288\\&- 26312 z + 553704 z^2 - 3461777 z^3+ 9763000 z^4 - 14401588 z^5 + 11527644 z^6 - 4728907 z^7 + 774416 z^8) \\&- 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (13 + 380 y^4 - 225 z+ 747 z^2 - 915 z^3 + 380 z^4 + y^3 (-915 + 584 z) \\&+ 9 y^2 (83 - 117 z + 64 z^2) + y (-225 + 654 z - 1053 z^2 + 584 z^3)) H(2, y)- 96 (-1 + y)^2 y (-1 + z)^2 z (y\\&+ z)^4 (4+ 16 y^4 - 22 z + 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z + 8 z^2)+ y (-22 + 48 z\\&- 51 z^2 + 20 z^3)) H(3, y)) - 2 (y + z)^2 (1728 y^{10} (-1 + z)^2 + 216 (-1 + z)^5 z^3 (-1 + 4 z) - 72 y^9 (-1\\&+ z)^2 (149 + 87 z) + y^8 (28080 - 43945 z - 17990 z^2 + 55603 z^3 - 21640 z^4) + y (-1 + z)^2 z^2 (144 - 3573 z \\&+ 10219 z^2- 12168 z^3 + 4234 z^4 + 864 z^5) - y^7 (39888 - 94511 z + 2851 z^2 + 137595 z^3 - 104887 z^4 \\&+ 19064 z^5) + y^6 (32832 - 125478 z+ 90408 z^2 + 113163 z^3 - 158918 z^4 + 46681 z^5 + 1096 z^6) - y^2 (-1 \\&+ z)^2 z (360 - 2430 z - 10125 z^2+ 18134 z^3 - 1460 z^4- 13140 z^5 + 4320 z^6) + y^5 (-15336 + 94486 z \\&- 141904 z^2 + 19649 z^3 + 66045 z^4 + 13557 z^5 - 53601 z^6+ 17104 z^7) + y^4 (3600- 38177 z + 94480 z^2 \\&- 70947 z^3+ 25180 z^4 - 94718 z^5 + 142546 z^6 - 75040 z^7 + 13184 z^8) + y^3 (-288+ 7227 z - 28965 z^2\\&+ 25131 z^3 + 4151 z^4 + 35390 z^5 - 108748 z^6 + 97128 z^7 - 33618 z^8 + 2592 z^9)) H(0, 0, y) - 2 (y \\&+ z)^2 (1728 y^9 (-1 + z)^2 (-1+ 3 z) - 216 (-1 + z)^6 z^3 (-1 + 4 z) + y^8 (9000 - 48470 z + 93492 z^2 - 78258 z^3 \\&+ 23552 z^4) + 4 y^7 (-4770 + 28897 z - 69529 z^2+ 79974 z^3 - 42772 z^4 + 8200 z^5) + y (-1 + z)^2 z^2 (144 - 3501 z \\&+ 19081 z^2 - 43239 z^3+ 50375 z^4 - 23976 z^5 + 1728 z^6)+ y^6 (20808 - 148735 z + 427794 z^2 - 614728 z^3\\&+ 447358 z^4 - 140145 z^5 + 9016 z^6) + y^5 (-12024 + 107821 z - 367983 z^2+ 619778 z^3- 507386 z^4 + 132177 z^5\\&+ 54601 z^6 - 26984 z^7) - y^2 (-1 + z)^2 z (360 - 2934 z - 12651 z^2 + 74708 z^3 - 142537 z^4+ 119942 z^5\\&- 36936 z^6 + 864 z^7) + y^4 (3312 - 41639 z + 174106 z^2 - 315241 z^3 + 188404 z^4 + 184665 z^5 - 356162 z^6\\&+ 199207 z^7 - 37336 z^8) + y^3 (-288 + 7155 z - 40995 z^2 + 60519 z^3 + 92277 z^4 - 437623 z^5 + 633399 z^6 \\&- 444135 z^7 + 146323 z^8- 16632 z^9)) H(0, 0, z) + 8 (-1 + y)^2 y (-1 + z) z (528 y^8 (-1+ z) - 3 (-1 + z)^2 z^4 (14\\&- 14 z + 3 z^2) + 6 y^7 (227 - 631 z+ 404 z^2) + 6 y^6 (-223 + 1245 z - 1758 z^2 + 738 z^3) + 3 y^5 (182 - 2102 z \\&+ 5517 z^2 - 4865 z^3 + 1284 z^4) + 2 y^2 z^2 (-294+ 1706 z - 2858 z^2 + 1581 z^3 + 225 z^4 - 354 z^5) + y z^3 (-384 \end{aligned}$$
$$\begin{aligned}&+ 1354 z- 1582 z^2 + 531 z^3 + 261 z^4 - 180 z^5) - 4 y^3 z (96- 1033 z + 2746 z^2 - 2667 z^3 + 666 z^4 + 180 z^5) \\&+ y^4 (-42 + 2398 z - 11683 z^2+ 18420 z^3 - 10149 z^4 + 1128 z^5)) H(0, 1, z)- 8 (-1 + y) y (-1 + z)^2 z (528 y^9 \\&+ 6 y^8 (-323 + 492 z) + 12 y^7 (237 - 866 z + 609 z^2) + 3 z^4 (-30 + 60 z - 49 z^2 + 19 z^3)+ 3 y^6 (-692 + 4784 z \\&- 7993 z^2 + 3540 z^3) + y z^3 (-144 + 1364 z - 1944 z^2 + 1374 z^3 - 405 z^4) + y^5 (732 - 9572 z + 30498 z^2\\&- 31161 z^3 + 9960 z^4) + y^2 z^2 (-204 + 3656 z - 8678 z^2 + 7902 z^3 - 3411 z^4 + 348 z^5) + 2 y^3 z (-72 + 2320 z \\&- 8830 z^2+ 11118 z^3 - 6117 z^4 + 1086 z^5) + y^4 (-90 + 2804 z - 18275 z^2 + 34641 z^3 - 24864 z^4 \\&+ 6048 z^5)) H(0, 2, y) + 264 (-1+ y)^2 y^2 (-1 + z)^2 z (y + z)^4 (16 y^3 + y^2 (-41 + 12 z) - 2 (7 - 6 z + 3 z^2) \\&+ 3 y (13 - 9 z + 4 z^2)) H(1, 0, y) - 8 (-1+ y)^2 y (-1 + z) z (-3 (-1 + z)^2 z^4 (30 - 30 z + 19 z^2) + y^7 (57 - 405 z \\&+ 348 z^2)+ 3 y^6 (-49 + 392 z - 939 z^2 + 592 z^3)+ 3 y^5 (60 - 516 z + 1941 z^2 - 2857 z^3 + 1356 z^4) + y z^3 (-144 \\&+ 956 z - 2180 z^2 + 2505 z^3 - 1581 z^4 + 444 z^5)+ y^2 z^2 (-204 + 1868 z - 6197 z^2 + 9312 z^3 - 6951 z^4 + 2160 z^5)\\&+ y^3 z (-144 + 1808 z - 8288 z^2 + 15567 z^3 - 13539 z^4+ 4548 z^5) + y^4 (-90 + 902 z - 5345 z^2+ 13260 z^3\\&- 14271 z^4 + 5472 z^5)) H(1, 0, z) + 2 (1728 y^{12} (-1 + z)^2 - 216 (-1+ z)^5 z^6 (-1 + 4 z) - 24 y^{11} (-1 + z)^2 (375 \\&+ 718 z) + y^{10} (19080 {+} 28289 z {-} 250122 z^2 {+} 338949 z^3 - 136304 z^4) + y (-1+ z)^2 z^5 (-8082 + 36428 z \\&- 80967 z^2{+} 91745 z^3 - 40992 z^4 {+} 1728 z^5) - y^9 (20808 + 63133 z - 748547 z^2 + 1624467 z^3- 1359901 z^4\\&+ 400256 z^5) + y^8 (12024 + 69787 z - 1130000 z^2 + 3636494 z^3 - 4922656 z^4 + 3035579 z^5 - 701120 z^6)\\&- y^2 (-1+ z)^2 z^4 (25944 - 171016 z + 438304 z^2 - 585767 z^3 + 364650 z^4 - 73560 z^5 + 864 z^6) - y^7 (3312\\&+ 52501 z - 1005911 z^2+ 4577790 z^3 - 9135618 z^4 + 9138769 z^5 - 4491307 z^6 + 860032 z^7) \end{aligned}$$
$$\begin{aligned}&+ y^6 (288 + 26312 z - 553704 z^2 +3461777 z^3 - 9763000 z^4+ 14401588 z^5 - 11527644 z^6 + 4728907 z^7 \\&- 774416 z^8) + y^5 z (-6066 + 175600 z - 1559775 z^2 + 6176973 z^3 - 12917254 z^4+ 15269476 z^5\\&- 10196989 z^6 + 3546779 z^7 - 488960 z^8) + y^4 z^2 (-23424 + 374888 z - 2225864 z^2 + 6614805 z^3 \!-\! 11116384 z^4\\&+ 10963698 z^5 - 6184528 z^6 + 1787581 z^7 - 190880 z^8)+ y^3 z^3 (-32844 + 401168 z- 1810731 z^2 + 4338377 z^3 \\&- 6108582 z^4+ 5103134 z^5 - 2392815 z^6+ 537669 z^7 - 35376 z^8)) H(1, 1, z)+ H(3, y) (96 (-1 + y)^2 y (-1 \\&+ z)^2 z (y+ z)^4 (4 + 16 y^4- 22 z+ 45 z^2 - 43 z^3+ 16 z^4 + y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z + 8 z^2)+ y (-22 \\&+ 48 z - 51 z^2+ 20 z^3)) H(0, 1, z)+ 96 (-1+ y)^2 y (-1 + z)^2 z (y + z)^4 (4 + 16 y^4 - 22 z + 45 z^2 - 43 z^3 + 16 z^4 \\&+ y^3 (-43+ 20 z)+ 3 y^2 (15 - 17 z + 8 z^2) + y (-22+ 48 z - 51 z^2 + 20 z^3)) H(1, 0, z) + 192 (-1 + y)^2 y (-1 \\&+ z)^2 z (y+ z)^4 (4 + 16 y^4 - 22 z + 45 z^2 - 43 z^3 + 16 z^4+ y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z + 8 z^2) + y (-22 \\&+ 48 z - 51 z^2+ 20 z^3)) H(1, 1, z)) - 8 (-1 + y) y (-1 + z)^2 z (528 y^9+ 6 y^8 (-323 + 492 z) + 12 y^7 (237 - 866 z \\&+ 609 z^2)+ 3 z^4 (-30 + 60 z - 49 z^2 + 19 z^3) + 3 y^6 (-692 + 4784 z - 7993 z^2+ 3540 z^3) + y z^3 (-144+ 1364 z \\&- 1944 z^2+ 1374 z^3 - 405 z^4) + y^5 (732 - 9572 z + 30498 z^2 - 31161 z^3 + 9960 z^4)+ y^2 z^2 (-204 + 3656 z\\&- 8678 z^2+ 7902 z^3 - 3411 z^4 + 348 z^5) + 2 y^3 z (-72 + 2320 z - 8830 z^2 + 11118 z^3 - 6117 z^4+ 1086 z^5) \\&+ y^4 (-90+ 2804 z - 18275 z^2 + 34641 z^3 - 24864 z^4 + 6048 z^5)) H(2, 0, y) + 2 (1728 y^{12} (-1 + z)^2 - 216 (-1\\&+ z)^5 z^6 (-1+ 4 z) - 24 y^{11} (-1 + z)^2 (375 + 718 z) + y^{10} (19080 {+} 28289 z - 250122 z^2 {+} 338949 z^3 {-} 136304 z^4) \end{aligned}$$
$$\begin{aligned}&+ y (-1+ z)^2 z^5 (-8082 {+} 36428 z - 80967 z^2 {+} 91745 z^3 - 40992 z^4 {+} 1728 z^5) - y^9 (20808 {+} 63133 z {-} 748547 z^2 \\&+ 1624467 z^3- 1359901 z^4 + 400256 z^5) + y^8 (12024 + 69787 z - 1130000 z^2 + 3636494 z^3 - 4922656 z^4 \\&+ 3035579 z^5 - 701120 z^6) - y^2 (-1+ z)^2 z^4 (25944 - 171016 z + 438304 z^2 - 585767 z^3 + 364650 z^4 - 73560 z^5 \\&+ 864 z^6) - y^7 (3312 + 52501 z - 1005911 z^2+ 4577790 z^3 - 9135618 z^4 + 9138769 z^5 - 4491307 z^6 \\&+ 860032 z^7) + y^6 (288 + 26312 z- 553704 z^2 + 3461777 z^3 - 9763000 z^4+ 14401588 z^5 - 11527644 z^6 \\&+ 4728907 z^7- 774416 z^8) + y^5 z (-6066+ 175600 z - 1559775 z^2 + 6176973 z^3 - 12917254 z^4+ 15269476 z^5 \\&- 10196989 z^6 + 3546779 z^7- 488960 z^8) + y^4 z^2 (-23424+ 374888 z - 2225864 z^2 + 6614805 z^3 - 11116384 z^4\\&+ 10963698 z^5 - 6184528 z^6 + 1787581 z^7 - 190880 z^8) + y^3 z^3 (-32844 + 401168 z- 1810731 z^2 + 4338377 z^3 \\&- 6108582 z^4+ 5103134 z^5 - 2392815 z^6 + 537669 z^7- 35376 z^8)) H(2, 2, y) + H(0, z) (-88 (-1+ y)^2 y (-1 \\&+ z) z (y + z)^4 (-5 (-1 + z)^2 (2- 2 z + z^2) + 5 y^3 (1 - 5 z + 4 z^2)+ 3 y^2 (-5 + 20 z - 24 z^2 + 8 z^3)+ 4 y (5 - 20 z\\&+ 33 z^2 - 29 z^3 + 11 z^4)) + 96 (-1+ y)^2 y (-1 + z)^2 z (y + z)^4 (1 + 8 y^4 - 9 z + 21 z^2 - 21 z^3 + 8 z^4 + y^3 (-21 \\&+ 8 z)+ 3 y^2 (7 - 7 z + 4 z^2) + y (-9 + 18 z- 21 z^2 + 8 z^3)) H(1, z)^2 - 264 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (y^3 (-1 \\&+ 4 z) + 4 y (-1 + z)^2 (-1 + 4 z) + 3 y^2 (1 - 5 z+ 4 z^2) + 2 (1 - 9 z + 21 z^2 - 21 z^3 + 8 z^4)) H(2, y) + 96 (-1 \\&+ y)^2 y (-1+ z)^2 z (y + z)^4 (8 y^4 + 2 y^3 (-11 + 6 z)+ 12 y^2 (2 - 3 z + 2 z^2) + y (-13 + 42 z - 57 z^2 + 24 z^3) \\&+ 3 (1 - 9 z + 21 z^2 - 21 z^3 + 8 z^4)) H(2, y)^2 + H(1, z) (32 (-1+ y)^2 y (-1 + z) z (-6 (-1 + z)^2 z^4 (1 - z + z^2) \\&+ 6 y^7 (1 - 10 z + 9 z^2) + 3 y^6 (-4 + 54 z - 155 z^2 + 104 z^3) + 3 y^5 (4- 52 z + 279 z^2 - 497 z^3 + 262 z^4) + y z^3 (30 \\&+ 8 z- 182 z^2 + 321 z^3 - 255 z^4 + 78 z^5) + y^2 z^2 (48 + 38 z - 650 z^2+ 1338 z^3 - 1185 z^4 + 408 z^5) + 2 y^3 z (15\\&+ 28 z - 475 z^2 + 1158 z^3 - 1185 z^4 + 453 z^5) + 2 y^4 (-3 + 22 z - 301 z^2+ 981 z^3 - 1260 z^4 + 552 z^5)) + 96 (-1\\&+ y)^2 y (-1 + z)^2 z^2 (y + z)^4 (-14 + 39 z - 41 z^2 + 16 z^3 + 6 y^2 (-1 + 2 z) + 3 y (4- 9 z + 4 z^2)) H(2, y)- 96 (-1 \end{aligned}$$
$$\begin{aligned}&+ y)^2 y (-1 + z)^2 z (y + z)^4 (4 + 16 y^4 - 22 z + 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43 + 20 z)+ 3 y^2 (15 - 17 z + 8 z^2) \\&+ y (-22 + 48 z - 51 z^2 + 20 z^3)) H(3, y)) - 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (16 y^4 + 4 y^3 (-11\\&+ 6 z) + 6 y^2 (8 - 9 z + 2 z^2) - 3 (-2 + 4 z - 3 z^2 + z^3) + y (-26 + 48 z - 33 z^2 + 12 z^3)) H(0, 0, y) - 96 (-1 \\&+ y)^2 y (-1+ z)^2 z^2 (y + z)^4 (-14 + 39 z - 41 z^2 + 16 z^3 + 6 y^2 (-1 + 2 z) + 3 y (4 - 9 z + 4 z^2)) H(0, 0, z) \\&- 96 (-1 + y)^2 y (-1+ z)^2 z (y + z)^4 (2 + 16 y^4 - 4 z + 3 z^2 - z^3 + 2 y^3 (-21 + 8 z) + 6 y^2 (7 - 6 z + 2 z^2)\\&+ y (-18 + 24 z - 15 z^2+ 4 z^3)) H(0, 1, z) - 96 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^4 (-4 + 18 z - 27 z^2 \\&+ 16 z^3+ y^2 (-2 + 8 z) + 2 y (2- 7 z + 2 z^2)) H(0, 2, y) + 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (2 {+} y^2 (3 {-} 9 z) {-} 4 z \\&+ 3 z^2 - z^3 + y^3 (-1 + 4 z) + y (-4+ 12 z - 9 z^2 + 4 z^3)) H(1, 0, z) - 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (4 \\&+ 16 y^4 - 22 z + 45 z^2- 43 z^3 + 16 z^4 + y^3 (-43+ 20 z) + 3 y^2 (15 - 17 z + 8 z^2) + y (-22 + 48 z - 51 z^2 \\&+ 20 z^3)) H(1, 1, z) - 96 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y+ z)^4 (-4 + 18 z - 27 z^2 + 16 z^3 + y^2 (-2 + 8 z) \\&+ 2 y (2 - 7 z + 2 z^2)) H(2, 0, y)- 192 (-1 + y)^2 y (-1 + z)^2 z (y+ z)^4 (8 y^4 + 2 y^3 (-11 + 6 z) + 12 y^2 (2 - 3 z \\&+ 2 z^2) + y (-13 + 42 z - 57 z^2+ 24 z^3) + 3 (1 - 9 z + 21 z^2 - 21 z^3+ 8 z^4)) H(2, 2, y)) + 264 (-1 + y)^2 y (-1 \\&+ z)^2 z (y + z)^4 (4 + 16 y^4 - 22 z+ 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43 + 20 z)+ 3 y^2 (15 - 17 z + 8 z^2) + y (-22 \\&+ 48 z - 51 z^2 + 20 z^3)) H(3, 2, y) + H(0, y) (-88 (-1+ y) y (-1 + z)^2 z (y + z)^4 (y^4 (-5+ 44 z) + 4 y^3 (5 - 29 z \\&+ 6 z^2) + 5 (-2 + 4 z- 3 z^2 + z^3) - 5 y (-6 + 16 z - 12 z^2+ 5 z^3) + y^2 (-35 + 132 z - 72 z^2+ 20 z^3)) \\&+ 48 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (6 - 26 z + 48 z^2 - 44 z^3 + 16 z^4 + 3 y^3 (-1 + 4 z) + 3 y^2 (3 - 11 z \\&+ 4 z^2)+ 6 y (-2 + 8 z - 9 z^2 + 4 z^3)) H(0, z)^2 + 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (3+ 24 y^4 - 13 z + 24 z^2\\&- 22 z^3 + 8 z^4+ 3 y^3 (-21 + 8 z) + 3 y^2 (21 - 19 z + 8 z^2) + 3 y (-9 + 14 z - 12 z^2 + 4 z^3)) H(1, z)^2+ 32 (-1 \\&+ y) y (-1 + z)^2 z (y^8 (-6+ 78 z) + 3 y^7 (6 - 85 z + 136 z^2) + 6 z^4 (-1 + 2 z - 2 z^2 + z^3) + 3 y^6 (-8 + 107 z \\&- 395 z^2 + 302 z^3) + 2 y z^3 (15 + 22 z- 78 z^2 + 81 z^3 - 30 z^4) + 2 y^5 (9 - 91 z + 669 z^2 - 1185 z^3 + 552 z^4)\\&+ y^2 z^2 (48 + 56 z - 602 z^2 + 837 z^3 - 465 z^4 + 54 z^5) + y^3 z (30 + 38 z - 950 z^2 + 1962 z^3 - 1491 z^4 + 312 z^5) \end{aligned}$$
$$\begin{aligned}&+ y^4 (-6 + 8 z - 650 z^2 + 2316 z^3 - 2520 z^4+ 786 z^5)) H(2, y) + 96 (-1 + y)^2 y (-1 + z)^2 z (y+ z)^4 (1 + 8 y^4\\&- 9 z + 21 z^2 - 21 z^3 + 8 z^4 + y^3 (-21 + 8 z) + 3 y^2 (7- 7 z + 4 z^2) + y (-9 + 18 z - 21 z^2 + 8 z^3)) H(2, y)^2\\&+ H(0, z) (-264 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (2 + y^2 (3 - 9 z)- 4 z + 3 z^2 - z^3 + y^3 (-1 + 4 z) + y (-4\\&+ 12 z - 9 z^2 + 4 z^3)) + 96 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^4 (16 y^3 + y^2 (-27 + 4 z) - 2 (2 - 2 z + z^2)\\&+ 2 y (9 - 7 z + 4 z^2)) H(1, z) + 96 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^4 (-4+ 18 z - 27 z^2 + 16 z^3 \\&+ y^2 (-2 + 8 z)+ 2 y (2 - 7 z + 2 z^2)) H(2, y)) + H(1, z) (-264 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (2+ 16 y^4 - 4 z \\&+ 3 z^2 - z^3+ 2 y^3 (-21 + 8 z) + 6 y^2 (7 - 6 z + 2 z^2) + y (-18 + 24 z - 15 z^2 + 4 z^3)) + 96 (-1 + y)^2 y^2 (-1\\&+ z)^2 z (y + z)^4 (16 y^3 + y^2 (-41 + 12 z) - 2 (7 - 6 z + 3 z^2) + 3 y (13 - 9 z + 4 z^2)) H(2, y) - 96 (-1 + y)^2 y (-1\\&+ z)^2 z (y + z)^4 (4 + 16 y^4 - 22 z + 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z + 8 z^2) + y (-22 \\&+ 48 z- 51 z^2 + 20 z^3)) H(3, y)) - 96 (-1 + y)^2 y^2 (-1 + z)^2 z (y + z)^4 (16 y^3 + y^2 (-41 + 12 z) - 2 (7 \\&- 6 z + 3 z^2) + 3 y (13- 9 z + 4 z^2)) H(0, 0, y) - 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (6 - 26 z + 48 z^2 - 44 z^3 \\&+ 16 z^4 + 3 y^3 (-1 + 4 z) + 3 y^2 (3- 11 z + 4 z^2) + 6 y (-2 + 8 z - 9 z^2 + 4 z^3)) H(0, 0, z) - 96 (-1 + y)^2 y (-1 \\&+ z)^2 z (-1 + y + z) (y + z)^4 (16 y^3 + y^2 (-27+ 4 z) - 2 (2 - 2 z + z^2) + 2 y (9 - 7 z + 4 z^2)) H(0, 1, z) + 96 (-1 \\&+ y)^2 y (-1+ z)^2 z (y+ z)^4 (2 + 16 y^4 - 4 z + 3 z^2- z^3 + 2 y^3 (-21 + 8 z) + 6 y^2 (7 - 6 z + 2 z^2) + y (-18 + 24 z \\&- 15 z^2 + 4 z^3)) H(0, 2, y) - 96 (-1 + y)^2 y^2 (-1 + z)^2 z (y+ z)^4 (16 y^3 + y^2 (-41 + 12 z) - 2 (7 - 6 z+ 3 z^2) \end{aligned}$$
$$\begin{aligned}&+ 3 y (13 - 9 z + 4 z^2)) H(1, 0, y) - 96 (-1 + y)^2 y (-1 + z)^2 z (-1 + y+ z) (y + z)^4 (16 y^3 + y^2 (-27 + 4 z)\\&- 2 (2 - 2 z + z^2) + 2 y (9 - 7 z+ 4 z^2)) H(1, 0, z) - 192 (-1 + y)^2 y (-1 + z)^2 z (y+ z)^4 (3 + 24 y^4 - 13 z\\&+ 24 z^2 - 22 z^3 + 8 z^4 + 3 y^3 (-21 + 8 z) + 3 y^2 (21 - 19 z + 8 z^2) + 3 y (-9 + 14 z - 12 z^2+ 4 z^3)) H(1, 1, z)\\&+ 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (2 + 16 y^4 - 4 z + 3 z^2 - z^3 {+} 2 y^3 (-21 + 8 z) {+} 6 y^2 (7 {-} 6 z+ 2 z^2) {+} y (-18\\&+ 24 z - 15 z^2 + 4 z^3)) H(2, 0, y) - 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (4 + 16 y^4 - 22 z + 45 z^2 - 43 z^3+ 16 z^4 \\&+ y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z + 8 z^2) + y (-22 + 48 z - 51 z^2 + 20 z^3)) H(2, 2, y) - 96 (-1 + y)^2 y (-1\\&+ z)^2 z (y + z)^4 (4 + 16 y^4 - 22 z + 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z + 8 z^2) + y (-22 \\&+ 48 z- 51 z^2 + 20 z^3)) H(3, 2, y)) + H(2, y) (-44 (-1 + y)^2 y (-1 + z)^2 z (y^7 (-9 + 84 z) + 3 y^6 (9 - 83 z \\&+ 144 z^2) - 9 z^4 (-2+ 4 z - 3 z^2 + z^3) + 3 y^5 (-12 + 92 z - 373 z^2 + 324 z^3) + y z^3 (-36 - 136 z + 276 z^2 - 249 z^3 \\&+ 84 z^4) + y^2 z^2 (-60- 292 z + 1053 z^2 - 1119 z^3 + 432 z^4) + y^3 z (-36 - 292 z + 1608 z^2 - 2175 z^3 + 972 z^4) \\&+ y^4 (18- 136 z + 1053 z^2 - 2175 z^3+ 1248 z^4)) - 96 (-1 + y)^2 y^2 (-1 + z)^2 z (y + z)^4 (16 y^3 + y^2 (-41 + 12 z) \\&- 2 (7- 6 z + 3 z^2) + 3 y (13 - 9 z+ 4 z^2)) H(0, 0, y) - 288 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (y^3 (-1 + 4 z)\\&+ 4 y (-1 + z)^2 (-1 + 4 z) + 3 y^2 (1 - 5 z + 4 z^2)+ 2 (1 - 9 z + 21 z^2 - 21 z^3 + 8 z^4)) H(0, 0, z) - 96 (-1 \\&+ y)^2 y (-1+ z)^2 z^2 (y + z)^4 (-14 + 39 z - 41 z^2 + 16 z^3+ 6 y^2 (-1 + 2 z) + 3 y (4 - 9 z + 4 z^2)) H(0, 1, z)\\&+ 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (2 + 16 y^4 - 4 z + 3 z^2 - z^3+ 2 y^3 (-21 + 8 z) + 6 y^2 (7 {-} 6 z+ 2 z^2) {+} y ({-}18 \\&+ 24 z - 15 z^2 + 4 z^3)) H(0, 2, y) - 96 (-1 + y)^2 y^2 (-1 + z)^2 z (y+ z)^4 (16 y^3 + y^2 (-41+ 12 z) - 2 (7 - 6 z\\&+ 3 z^2) + 3 y (13 - 9 z + 4 z^2)) H(1, 0, y) - 96 (-1 + y)^2 y (-1 + z)^2 z^2 (y+ z)^4 (-14 + 39 z- 41 z^2 + 16 z^3 \\&+ 6 y^2 (-1+ 2 z) + 3 y (4 - 9 z + 4 z^2)) H(1, 0, z) + 192 (-1 + y)^2 y (-1 + z)^2 z (y+ z)^4 (13 + 380 y^4 - 225 z \\&+ 747 z^2- 915 z^3 + 380 z^4 + y^3 (-915 + 584 z) + 9 y^2 (83 - 117 z + 64 z^2) + y (-225+ 654 z- 1053 z^2 \\&+ 584 z^3)) H(1, 1, z) + 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (2 + 16 y^4 - 4 z + 3 z^2- z^3 + 2 y^3 (-21 + 8 z)\\&+ 6 y^2 (7 - 6 z + 2 z^2) + y (-18 + 24 z - 15 z^2 + 4 z^3)) H(2, 0, y) - 96 (-1 + y)^2 y (-1+ z)^2 z (y + z)^4 (4\\&+ 16 y^4 - 22 z+ 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z + 8 z^2) + y (-22 + 48 z- 51 z^2 \\&+ 20 z^3)) H(2, 2, y)- 96 (-1+ y)^2 y (-1 + z)^2 z (y + z)^4 (4 + 16 y^4 - 22 z + 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43 \end{aligned}$$
$$\begin{aligned}&+ 20 z)+ 3 y^2 (15 - 17 z + 8 z^2) + y (-22+ 48 z - 51 z^2 + 20 z^3)) H(3, 2, y)) + H(1, z) (-44 (-1 + y)^2 y (-1 \\&+ z)^2 z (y^7 (-9+ 84 z) + 3 y^6 (9 - 83 z + 144 z^2)- 9 z^4 (-2 + 4 z - 3 z^2 + z^3) + 3 y^5 (-12 + 92 z - 373 z^2 \\&+ 324 z^3) + y z^3 (-36- 136 z + 276 z^2 - 249 z^3 + 84 z^4)+ y^2 z^2 (-60 - 292 z + 1053 z^2 - 1119 z^3 + 432 z^4) \\&+ y^3 z (-36 - 292 z + 1608 z^2- 2175 z^3 + 972 z^4) + y^4 (18 - 136 z + 1053 z^2 - 2175 z^3 + 1248 z^4)) - 96 (-1 \\&+ y)^2 y (-1 + z)^2 z (y + z)^4 (13 + 380 y^4 - 225 z+ 747 z^2 - 915 z^3 + 380 z^4+ y^3 (-915 + 584 z) + 9 y^2 (83 \\&- 117 z + 64 z^2) + y (-225+ 654 z - 1053 z^2 + 584 z^3)) H(2, y)^2 + 264 (-1 + y)^2 y (-1+ z)^2 z (y + z)^4 (4 \\&+ 16 y^4 - 22 z + 45 z^2 - 43 z^3+ 16 z^4 + y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z + 8 z^2) + y (-22 + 48 z- 51 z^2 \\&+ 20 z^3)) H(3, y) - 96 (-1 + y)^2 y (-1+ z)^2 z (y + z)^4 (4 + 16 y^4 - 22 z+ 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43 + 20 z) \\&+ 3 y^2 (15 - 17 z + 8 z^2) + y (-22 + 48 z - 51 z^2 + 20 z^3)) H(2, y) H(3, y)- 288 (-1 + y)^2 y (-1 + z)^2 z (y \\&+z)^4 (2 + 16y^4- 4 z + 3 z^2 - z^3+ 2 y^3 (-21 + 8 z) + 6 y^2 (7 - 6 z + 2 z^2) + y (-18+ 24 z - 15 z^2 \\&+ 4 z^3)) H(0, 0, y) - 96 (-1 + y)^2 y (-1+ z)^2 z^2 (y + z)^4 (-14+ 39 z - 41 z^2 + 16 z^3 + 6 y^2 (-1+ 2 z) + 3 y (4 \\&- 9 z + 4 z^2)) H(0, 0, z)- 96 (-1 + y)^2 y (-1+ z)^2 z (y + z)^4 (2 + 16 y^4 - 4 z + 3 z^2 - z^3 + 2 y^3 (-21 + 8 z) \\&+ 6 y^2 (7 - 6 z + 2 z^2) + y (-18 + 24 z - 15 z^2+ 4 z^3)) H(0, 1, z) - 96 (-1 + y)^2 y^2 (-1 + z)^2 z (y + z)^4 (16 y^3 \\&+ y^2 (-41 + 12 z) - 2 (7 - 6 z + 3 z^2) + 3 y (13 - 9 z+ 4 z^2)) H(0, 2, y) + 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (4 \\&+ 16 y^4 - 22 z + 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43 + 20 z)+ 3 y^2 (15 - 17 z + 8 z^2) + y (-22 + 48 z - 51 z^2\\&+ 20 z^3)) H(0, 3, y) + 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (2 + y^2 (3 - 9 z)- 4 z + 3 z^2 - z^3 + y^3 (-1 + 4 z) \end{aligned}$$
$$\begin{aligned}&+ y (-4 + 12 z - 9 z^2 + 4 z^3)) H(1, 0, z) - 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (4 + 16 y^4- 22 z + 45 z^2 - 43 z^3 \\&+ 16 z^4 + y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z + 8 z^2) + y (-22 + 48 z - 51 z^2 + 20 z^3)) H(1, 1, z)- 96 (-1 \\&+ y)^2 y^2 (-1+ z)^2 z (y + z)^4 (16 y^3 + y^2 (-41 + 12 z) - 2 (7 - 6 z + 3 z^2) + 3 y (13 - 9 z + 4 z^2)) H(2, 0, y)\\&+ 192 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (13 + 380 y^4 - 225 z + 747 z^2 - 915 z^3 + 380 z^4 + y^3 (-915 + 584 z) \\&+ 9 y^2 (83 - 117 z+ 64 z^2) + y (-225 + 654 z - 1053 z^2 + 584 z^3)) H(2, 2, y) + 96 (-1 + y)^2 y (-1 + z)^2 z (y \\&+ z)^4 (4 + 16 y^4 - 22 z + 45 z^2- 43 z^3 + 16 z^4 + y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z + 8 z^2) + y (-22 + 48 z \\&- 51 z^2 + 20 z^3)) H(2, 3, y) + 96 (-1 + y)^2 y(-1+ z)^2 z (y + z)^4 (4 + 16 y^4 - 22 z + 45 z^2 - 43 z^3 + 16 z^4 \\&+ y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z + 8 z^2) + y (-22 + 48 z- 51 z^2 + 20 z^3)) H(3, 0, y) + 96 (-1 + y)^2 y (-1 \\&+ z)^2 z (y + z)^4 (4+ 16 y^4 - 22 z + 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43+ 20 z) + 3 y^2 (15 - 17 z + 8 z^2) + y (-22 \\&+ 48 z- 51 z^2 + 20 z^3)) H(3, 2, y)) + 48 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (56+ 596 y^4 + 34 z - 396 z^2 + 550 z^3 \\&- 244 z^4 + y^3 (-1661 + 1420 z) + 3 y^2 (511 - 769 z + 204 z^2) - 4 y (131 - 237 z + 51 z^2+ 38 z^3)) H(0, 0, 0, y)\\&- 48 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (-56 + 244 y^4 + 524 z- 1533 z^2 + 1661 z^3 - 596 z^4+ 2 y^3 (-275 + 76 z) \\&+ y^2 (396 + 204 z - 612 z^2) - y (34 + 948 z - 2307 z^2 + 1420 z^3)) H(0, 0, 0, z) + 96 (-1 + y)^2 y (-1+ z)^2 z (y\\&+ z)^4 (2 + 32 y^4 - 4 z + 3 z^2 - z^3 + y^3 (-83 + 28 z) + 3 y^2 (27 - 21 z + 8 z^2) + y (-32 + 36 z - 21 z^2\\&+ 4 z^3)) H(0, 0, 1, z) - 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (32 y^4 + y^3 (-85 + 36 z) + 3 y^2 (29 - 27 z + 8 z^2) \end{aligned}$$
$$\begin{aligned}&- 3 (-2 + 4 z- 3 z^2 + z^3) + y (-40 + 60 z - 39 z^2 + 12 z^3)) H(0, 0, 2, y) + 96 (-1 + y)^2 y^2 (-1 + z)^2 z (y \\&+ z)^4 (16 y^3 + y^2 (-41 + 12 z)- 2 (7 - 6 z + 3 z^2) + 3 y (13 - 9 z + 4 z^2)) H(0, 1, 0, y) + 96 (-1 + y)^2 y (-1 \\&+ z)^2 z (y + z)^4 (-2 + 16 y^4 + 8 y^3 (-5 + z)+ 4 z - 3 z^2 + z^3 + 6 y^2 (6 - 3 z + 2 z^2) + y (-10 + 3 z^2 \\&- 4 z^3)) H(0, 1, 0, z) + 96 (-1 + y)^2 y (-1 + z)^2 z (y+ z)^4 (32 y^4 + y^3 (-85 + 36 z) + 3 y^2 (29 - 27 z + 8 z^2)\\&- 3 (-2 + 4 z - 3 z^2 + z^3) + y (-40 + 60 z - 39 z^2+ 12 z^3)) H(0, 1, 1, z) - 96 (-1 + y)^2 y (-1 + z)^2 z (y \\&+ z)^4 (32 y^4 + y^3 (-85 + 36 z) + 3 y^2 (29 - 27 z + 8 z^2) - 3 (-2+ 4 z - 3 z^2 + z^3) + y (-40 + 60 z - 39 z^2 \\&+ 12 z^3)) H(0, 2, 0, y)- 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (2 + 32 y^4 - 4 z+ 3 z^2 - z^3 + y^3 (-83 + 28 z) \\&+ 3 y^2 (27- 21 z + 8 z^2) + y (-32 + 36 z - 21 z^2+ 4 z^3)) H(0, 2, 2, y) + 96 (-1 + y)^2 y (-1+ z)^2 z (y + z)^4 (4 \\&+ 16 y^4 - 22 z + 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43 + 20 z)+ 3 y^2 (15 - 17 z + 8 z^2) + y (-22 + 48 z- 51 z^2 \\&+ 20 z^3)) H(0, 3, 2, y) + 192 (-1 + y)^2 y^2 (-1+ z)^2 z (y + z)^4 (16 y^3 + y^2 (-41 + 12 z) - 2 (7 - 6 z + 3 z^2) \\&+ 3 y (13 - 9 z + 4 z^2)) H(1, 0, 0, y)- 288 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (2+ y^2 (3 - 9 z) - 4 z + 3 z^2 - z^3 \\&+ y^3 (-1+ 4 z)+ y (-4 + 12 z - 9 z^2 + 4 z^3)) H(1, 0, 0, z) + 96 (-1 + y)^2 y (-1+ z)^2 z (y + z)^4 (2 + 16 y^4 - 4 z \\&+ 3 z^2 - z^3+ 2 y^3 (-21 + 8 z) + 6 y^2 (7 - 6 z + 2 z^2) + y (-18 + 24 z - 15 z^2 + 4 z^3)) H(1, 0, 1, z)+ 96 (-1 \\&+ y)^2 y^2 (-1+ z)^2 z (y+ z)^4 (16 y^3 + y^2 (-41 + 12 z)- 2 (7 - 6 z + 3 z^2) + 3 y (13 - 9 z + 4 z^2)) H(1, 0, 2, y) \\&- 96 (-1+ y)^2 y (-1 + z)^2 z (y+ z)^4 (2 + y^2 (3 - 9 z) - 4 z + 3 z^2 - z^3 + y^3 (-1 + 4 z) + y (-4 + 12 z - 9 z^2 \\&+ 4 z^3)) H(1, 1, 0, z) + 96 (-1 + y)^2 y (-1+ z)^2 z (y + z)^4 (30 + 776 y^4 - 472 z + 1539 z^2 - 1873 z^3 + 776 z^4 \\&+ y^3 (-1873 + 1188 z) + 3 y^2 (513 - 719 z + 392 z^2)+ y (-472 + 1356 z - 2157 z^2 + 1188 z^3)) H(1, 1, 1, z)\\&+ 96 (-1 + y)^2 y^2 (-1 + z)^2 z (y + z)^4 (16 y^3 + y^2 (-41 + 12 z) - 2 (7- 6 z + 3 z^2) + 3 y (13 - 9 z \end{aligned}$$
$$\begin{aligned}&+ 4 z^2)) H(1, 2, 0, y) - 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (32 y^4 + y^3 (-85 + 36 z) + 3 y^2 (29- 27 z + 8 z^2)\\&- 3 (-2 + 4 z - 3 z^2 + z^3) + y (-40 + 60 z - 39 z^2 + 12 z^3)) H(2, 0, 0, y) - 96 (-1 + y)^2 y (-1 + z)^2 z (y\\&+ z)^4 (2 + 32 y^4 - 4 z + 3 z^2 - z^3 + y^3 (-83 + 28 z) + 3 y^2 (27 - 21 z + 8 z^2) + y (-32 + 36 z - 21 z^2\\&+ 4 z^3)) H(2, 0, 2, y) + 96 (-1 + y)^2 y^2 (-1 + z)^2 z (y + z)^4 (16 y^3 + y^2 (-41 + 12 z) - 2 (7 - 6 z + 3 z^2) + 3 y (13 \\&- 9 z+ 4 z^2)) H(2, 1, 0, y) - 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (2 + 32 y^4 - 4 z + 3 z^2 - z^3 + y^3 (-83 + 28 z)\\&+ 3 y^2 (27- 21 z + 8 z^2) + y (-32 + 36 z - 21 z^2 + 4 z^3)) H(2, 2, 0, y) + 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (30 \\&+ 776 y^4 - 472 z+ 1539 z^2 - 1873 z^3 + 776 z^4 + y^3 (-1873 + 1188 z) + 3 y^2 (513 - 719 z + 392 z^2) + y (-472 \\&+ 1356 z - 2157 z^2+ 1188 z^3)) H(2, 2, 2, y) + 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (4 + 16 y^4 - 22 z + 45 z^2 - 43 z^3\\&+ 16 z^4 + y^3 (-43 + 20 z)+ 3 y^2 (15 - 17 z + 8 z^2) + y (-22 + 48 z - 51 z^2 + 20 z^3)) H(2, 3, 2, y) + 96 (-1 \\&+ y)^2 y (-1 + z)^2 z (y + z)^4 (4 + 16 y^4- 22 z + 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z + 8 z^2) \\&+ y (-22 + 48 z - 51 z^2 + 20 z^3)) H(3, 0, 2, y)+ 96 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (4 + 16 y^4 - 22 z + 45 z^2 \\&- 43 z^3 + 16 z^4+ y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z + 8 z^2)+ y (-22 + 48 z - 51 z^2 + 20 z^3)) H(3, 2, 0, y) \\&+ 192 (-1 + y)^2 y (-1 + z)^2 z (y + z)^4 (4+ 16 y^4 - 22 z + 45 z^2- 43 z^3+ 16 z^4 + y^3 (-43 + 20 z)\\&+ 3 y^2 (15 - 17 z + 8 z^2) + y (-22 + 48 z - 51 z^2 + 20 z^3)) H(3, 2, 2, y)\Bigg \}\Big / \Big (192 (-1 + y)^2 y^2 (-1\\&+ z)^2 z^2 (-1 + y + z) (y + z)^4\Big ); \end{aligned}$$
$$\begin{aligned} \mathcal {A}_{3;C_{F}^{2}}^{(2)}&= \Bigg \{-18 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (2 + y^2 (3 - 9 z) - 4 z + 3 z^2 - z^3 + y^3 (-1 + 4 z) + y (-4 + 12 z - 9 z^2 \\&\qquad + 4 z^3))- 12 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-44 + 528 y^3 + 66 z - 99 z^2 + 64 z^3 + y^2 (-829 \\&\qquad + 412 z)+ 2 y (187 - 176 z+ 58 z^2)) H(0, y)^3 - 12 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-44 + 64 y^3 \\&\qquad + 374 z- 829 z^2+ 528 z^3 + y^2 (-99+ 116 z) + y (66 - 352 z + 412 z^2)) H(0, z)^3 - 12 (-1 + y)^2 y (-1 + z)^2 z (-1\\&\qquad + y + z) (y+ z)^2 (4 + 72 y^3 + 46 z - 131 z^2+ 72 z^3 + y^2 (-131 + 108 z) + 2 y (23 - 50 z + 54 z^2)) H(1, z)^3 \end{aligned}$$
$$\begin{aligned}&- 2 (432 y^{10} (-1 + z)^2 - 54 (-1 + z)^5 z^4 (-1 + 4 z)+ 2 y^9 (-1 + z)^2 (-1125 + 1321 z) + 3 y^8 (1590 - 7130 z \\&+ 10312 z^2 - 5603 z^3 + 822 z^4) + y^7 (-5202 + 29970 z - 47113 z^2+ 16349 z^3 + 14834 z^4 - 8838 z^5) + y (-1 \\&+ z)^2 z^3 (-1653 + 4845 z - 5811 z^2 + 4198 z^3- 2002 z^4 + 432 z^5) + y^6 (3006- 18611 z + 14103 z^2 \\&+ 65692 z^3 - 134393 z^4 + 90425 z^5 - 20168 z^6) - y^2 (-1 + z)^2 z^2 (792 - 14109 z + 32355 z^2 - 27545 z^3\\&+ 10016 z^4 - 1898 z^5 + 216 z^6) + y^5 (-828 + 945 z + 35948 z^2 - 178242 z^3 + 329525 z^4 - 282687 z^5 + 110081 z^6 \\&- 14742 z^7)+ y^4 (72 + 4209 z - 39045 z^2 + 174583 z^3 - 372816 z^4 + 403037 z^5 - 220595 z^6 + 54578 z^7 \\&- 4050 z^8) + y^3 z (-1401 + 13065 z- 78255 z^2 + 213625 z^3 - 291633 z^4 + 209152 z^5 - 75802 z^6 + 11847 z^7 \\&- 598 z^8)) H(2, y)^2- 12 (-1 + y)^2 y (-1 + z)^2 z (-1+ y + z) (y + z)^2 (4 + 72 y^3 + 46 z - 131 z^2 + 72 z^3 \\&+ y^2 (-131 + 108 z)+ 2 y (23 - 50 z + 54 z^2)) H(2, y)^3+ H(0, z)^2 (-108 (-1 + z)^6 z^3 (-1 + 4 z) - 4 y^9 (-1 \\&+ z)^2 (216+ 215 z) + y^8 (4500 - 8947 z - 426 z^2 + 9495 z^3 - 4692 z^4)+ y (-1 + z)^3 z^2 (-72 + 2469 z - 8130 z^2 \\&+ 15633 z^3 - 12928 z^4 + 864 z^5) - y^7 (9540 - 30281 z + 21427 z^2 + 17363 z^3- 25789 z^4 + 7740 z^5)\\&- 2 y^6 (-5202 + 24062 z - 33217 z^2 + 1427 z^3 + 33635 z^4 - 28049 z^5 + 7274 z^6) - y^2 (-1 + z)^2 z (180\\&+ 114 z - 13297 z^2 + 48726 z^3 - 88199 z^4 + 76698 z^5 - 22076 z^6 + 432 z^7) - 4 y^5 (1503 - 9820 z + 19651 z^2 \\&- 5048 z^3- 33560 z^4 + 51210 z^5 - 31336 z^6 + 7400 z^7) + y^4 (1656 - 15965 z + 40998 z^2 + 3632 z^3 - 193426 z^4 \\&+ 388782 z^5 - 361522 z^6+ 164423 z^7 - 28648 z^8) - y^3 (144 - 2787 z + 8149 z^2 + 23010 z^3 - 166174 z^4 \end{aligned}$$
$$\begin{aligned}&+ 387958 z^5- 474394 z^6 + 314077 z^7 - 100103 z^8+ 10120 z^9) + 48 (-1 + y)^2 y (y^2 + 2 y (-1 + z) + 2 (-1 \\&+ z)^2) (-1 + z)^2 z (-1 + y+ z) (y + z)^2 (-1 + 4 z) H(1, z) + 48 (-1+ y)^2 y (y^2 + 2 y (-1 + z) + 2 (-1 \\&+ z)^2) (-1 + z)^2 z (-1 + y+ z) (y + z)^2 (-1+ 4 z) H(2, y)) + H(0, y)^2 (864 y^{10} (-1 + z)^2+ 108 (-1 + z)^5 z^3 (-1\\&+ 4 z) - 4 y^9 (-1 + z)^2 (1341 + 1234 z)+ y^8 (14040 - 14991 z - 32938 z^2 + 54743 z^3 - 20800 z^4)+ y^7 (-19944 \\&+ 36561 z + 52567 z^2 - 160807 z^3 + 117263 z^4 - 25640 z^5)- y (-1 + z)^2 z^2 (-72 + 2577 z - 8383 z^2 + 13377 z^3\\&- 10501 z^4 + 3020 z^5) - 4 y^6 (-4104 + 13505 z + 4189 z^2 - 53569 z^3 + 65725 z^4 - 30346 z^5 + 4627 z^6) + y^2 (-1\\&+ z)^2 z(-180- 366 z + 14249 z^2 - 35168 z^3 + 44729 z^4 - 26794 z^5 + 4744 z^6) - 2 y^5 (3834- 21096 z + 12153 z^2\\&+ 79661 z^3 - 164736 z^4+ 132075 z^5 - 49685 z^6 + 7794 z^7) + y^4 (1800 - 16449 z + 20344 z^2 + 84562 z^3 \\&- 275038 z^4 + 340574 z^5 - 219676 z^6 + 73813 z^7- 9876 z^8) - y^3 (144 - 2823 z + 4349 z^2 + 40704 z^3 \\&- 163328 z^4 + 272002 z^5 - 250136 z^6 + 128747 z^7 - 31815 z^8 + 2156 z^9)+ 48 (-1 + y)^2 y (-1 + 4 y) (-1\\&+ z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z) - 2 z + z^2) H(1, z) + 48 (-1 + y)^2 y (-1+ 4 y) (-1\\&+ z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z) - 2 z + z^2) H(2, y)) + H(1, z)^2 (-2 (432 y^{10} (-1 + z)^2\\&- 54 (-1 + z)^5 z^4 (-1 + 4 z) + 2 y^9 (-1 + z)^2 (-1125 + 1321 z) + 3 y^8 (1590 - 7130 z + 10312 z^2 - 5603 z^3 \\&+ 822 z^4)+ y^7 (-5202 + 29970 z - 47113 z^2 + 16349 z^3 + 14834 z^4 - 8838 z^5) + y (-1 + z)^2 z^3 (-1653 \\&+ 4845 z - 5811 z^2 + 4198 z^3- 2002 z^4 + 432 z^5) + y^6 (3006 - 18611 z + 14103 z^2 + 65692 z^3 - 134393 z^4 \\&+ 90425 z^5 - 20168 z^6) - y^2 (-1 + z)^2 z^2 (792- 14109 z + 32355 z^2 - 27545 z^3 + 10016 z^4 - 1898 z^5 + 216 z^6) \\&+ y^5 (-828 + 945 z + 35948 z^2 - 178242 z^3 + 329525 z^4- 282687 z^5 + 110081 z^6 - 14742 z^7) + y^4 (72 + 4209 z \\&- 39045 z^2 + 174583 z^3 - 372816 z^4 + 403037 z^5 - 220595 z^6 + 54578 z^7 - 4050 z^8) + y^3 z (-1401 + 13065 z \\&- 78255 z^2 + 213625 z^3 - 291633 z^4 + 209152 z^5 - 75802 z^6 + 11847 z^7 - 598 z^8)) - 60 (-1+ y)^2 y (-1 \\&+ z)^2 z (-1 + y + z) (y + z)^2 (-4 + 56 y^3 + 50 z - 109 z^2 + 56 z^3 + y^2 (-109 + 84 z) + y (50 - 92 z\\&+ 84 z^2)) H(2, y) - 96 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-4 + 8 y^3 + 14 z - 19 z^2 + 8 z^3 + y^2 (-19 \\&+ 12 z)+ 2 y (7 - 10 z + 6 z^2)) H(3, y)) - 2 (864 y^{10} (-1 + z)^2 + 108 (-1 + z)^5 z^3 (-1 + 4 z) - 4 y^9 (-1 \\&+ z)^2 (1341 + 1234 z)+ y^8 (14040 - 14991 z - 32938 z^2 + 54743 z^3 - 20800 z^4) + y^7 (-19944 + 36561 z \\&+ 52567 z^2 - 160807 z^3 + 117263 z^4 - 25640 z^5)- y (-1 + z)^2 z^2 (-72 + 2577 z - 8383 z^2 + 13377 z^3 - 10501 z^4 \\&+ 3020 z^5) - 4 y^6 (-4104 + 13505 z + 4189 z^2 - 53569 z^3+ 65725 z^4 - 30346 z^5 + 4627 z^6) + y^2 (-1 \end{aligned}$$
$$\begin{aligned}&+ z)^2 z (-180 - 366 z + 14249 z^2 - 35168 z^3 + 44729 z^4 - 26794 z^5 + 4744 z^6)- 2 y^5 (3834 - 21096 z + 12153 z^2 \\&+ 79661 z^3 - 164736 z^4 + 132075 z^5 - 49685 z^6 + 7794 z^7) + y^4 (1800 - 16449 z + 20344 z^2+ 84562 z^3 \\&- 275038 z^4 + 340574 z^5 - 219676 z^6 + 73813 z^7 - 9876 z^8) - y^3 (144 - 2823 z + 4349 z^2 + 40704 z^3 \\&- 163328 z^4+ 272002 z^5 - 250136 z^6 + 128747 z^7 - 31815 z^8 + 2156 z^9)) H(0, 0, y) + 2 (108 (-1 + z)^6 z^3 (-1\\&+ 4 z) + 4 y^9 (-1 + z)^2 (216+ 215 z) + y^8 (-4500 + 8947 z + 426 z^2 - 9495 z^3 + 4692 z^4) - y (-1 + z)^3 z^2 (-72\\&+ 2469 z - 8130 z^2 + 15633 z^3 - 12928 z^4+ 864 z^5) + y^7 (9540 - 30281 z + 21427 z^2 + 17363 z^3 - 25789 z^4 \\&+ 7740 z^5) + 2 y^6 (-5202 + 24062 z - 33217 z^2 + 1427 z^3+ 33635 z^4 - 28049 z^5 + 7274 z^6) + y^2 (-1 + z)^2 z (180 \\&+ 114 z - 13297 z^2 + 48726 z^3 - 88199 z^4 + 76698 z^5 - 22076 z^6+ 432 z^7) + 4 y^5 (1503 - 9820 z + 19651 z^2 \\&- 5048 z^3 - 33560 z^4 + 51210 z^5 - 31336 z^6 + 7400 z^7) + y^4 (-1656 + 15965 z- 40998 z^2 - 3632 z^3 + 193426 z^4 \\&- 388782 z^5 + 361522 z^6 - 164423 z^7 + 28648 z^8) + y^3 (144 - 2787 z + 8149 z^2 + 23010 z^3 - 166174 z^4\\&+ 387958 z^5 - 474394 z^6 + 314077 z^7 - 100103 z^8 + 10120 z^9)) H(0, 0, z) - 48 (-1 + y)^2 y^2 z^2 (-1 + y + z) (y\\&+ z)^2 (-12 + 30 z - 26 z^2 + 8 z^3 + 3 y (4 - 9 z + 4 z^2)) H(0, 1, z) - 48 y^2 (-1 + z)^2 z^2 (-1 + y + z) (y + z)^2 (8 y^3 \\&+ y (30- 27 z) + 12 (-1 + z) + 2 y^2 (-13 + 6 z)) H(0, 2, y) - 48 (-1 + y)^2 y^2 z^2 (-1 + y + z) (y + z)^2 (-12 \\&+ 30 z - 26 z^2 + 8 z^3+ 3 y (4 - 9 z + 4 z^2)) H(1, 0, z) + 4 (432 y^{10} (-1 + z)^2 - 54 (-1 + z)^5 z^4 (-1 + 4 z) \\&+ 2 y^9 (-1 + z)^2 (-1125 + 1321 z)+ 3 y^8 (1590 - 7130 z + 10312 z^2 - 5603 z^3 + 822 z^4) + y^7 (-5202 + 29970 z \\&- 47113 z^2 + 16349 z^3 + 14834 z^4 - 8838 z^5)+ y (-1 + z)^2 z^3 (-1653 + 4845 z - 5811 z^2 + 4198 z^3 - 2002 z^4 \\&+ 432 z^5) + y^6 (3006 - 18611 z + 14103 z^2 + 65692 z^3\\ \end{aligned}$$
$$\begin{aligned}&- 134393 z^4 + 90425 z^5 - 20168 z^6) - y^2 (-1 + z)^2 z^2 (792 - 14109 z + 32355 z^2 - 27545 z^3 + 10016 z^4 \\&- 1898 z^5 + 216 z^6)+ y^5 (-828 + 945 z + 35948 z^2 - 178242 z^3 + 329525 z^4 - 282687 z^5 + 110081 z^6 \\&- 14742 z^7) + y^4 (72 + 4209 z - 39045 z^2+ 174583 z^3 - 372816 z^4 + 403037 z^5 - 220595 z^6 + 54578 z^7\\&- 4050 z^8) + y^3 z (-1401 + 13065 z - 78255 z^2 + 213625 z^3- 291633 z^4 + 209152 z^5 - 75802 z^6 + 11847 z^7 \\&- 598 z^8)) H(1, 1, z) + 192 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-4+ 8 y^3 + 14 z - 19 z^2 + 8 z^3 \\&+ y^2 (-19 + 12 z) + 2 y (7 - 10 z + 6 z^2)) H(3, y) H(1, 1, z) + H(0, y) (96 (-1 + y)^2 y (-1+ 4 y) (-1 + z)^2 z (-1 \\&+ y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z) - 2 z + z^2) H(1, z)^2 + 48 y^2 (-1 + z)^2 z^2 (-1 + y + z) (y+ z)^2 (8 y^3 \\&+ y (30 - 27 z) + 12 (-1 + z) + 2 y^2 (-13 + 6 z)) H(2, y) + 96 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 + y \\&+ z) (y+ z)^2 (2 + 2 y^2 + 2 y (-2 + z) - 2 z + z^2) H(1, z) H(2, y) - 192 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 \\&+ y + z) (y + z)^2 (2+ 2 y^2 + 2 y (-2 + z) - 2 z + z^2) H(1, 1, z)) - 48 y^2 (-1 + z)^2 z^2 (-1 + y + z) (y + z)^2 (8 y^3 \\&+ y (30 - 27 z) + 12 (-1 + z)+ 2 y^2 (-13 + 6 z)) H(2, 0, y) + 4 (432 y^{10} (-1 + z)^2 - 54 (-1 + z)^5 z^4 (-1 + 4 z) \\&+ 2 y^9 (-1 + z)^2 (-1125 + 1321 z)+ 3 y^8 (1590 - 7130 z + 10312 z^2 - 5603 z^3 + 822 z^4) + y^7 (-5202 + 29970 z \\&- 47113 z^2 + 16349 z^3 + 14834 z^4 - 8838 z^5)+ y (-1 + z)^2 z^3 (-1653 + 4845 z - 5811 z^2 + 4198 z^3 - 2002 z^4 \\&+ 432 z^5) + y^6 (3006 - 18611 z + 14103 z^2 + 65692 z^3- 134393 z^4 + 90425 z^5 - 20168 z^6) - y^2 (-1 \\&+ z)^2 z^2 (792 - 14109 z + 32355 z^2 - 27545 z^3 + 10016 z^4 - 1898 z^5 + 216 z^6)+ y^5 (-828 + 945 z + 35948 z^2 \\&- 178242 z^3 + 329525 z^4 - 282687 z^5 + 110081 z^6 - 14742 z^7) + y^4 (72 + 4209 z - 39045 z^2\\ \end{aligned}$$
$$\begin{aligned}&+ 174583 z^3 - 372816 z^4 + 403037 z^5 - 220595 z^6 + 54578 z^7 - 4050 z^8) + y^3 z (-1401 + 13065 z - 78255 z^2 \\&+ 213625 z^3- 291633 z^4 + 209152 z^5 - 75802 z^6 + 11847 z^7 - 598 z^8)) H(2, 2, y) + H(0, z) (96 (-1+ y)^2 y (y^2\\&+ 2 y (-1 + z) + 2 (-1+ z)^2) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-1 + 4 z) H(2, y)^2 + H(1, z) (48 (-1 \\&+ y)^2 y^2 z^2 (-1 + y + z) (y + z)^2 (-12 + 30 z- 26 z^2 + 8 z^3 + 3 y (4 - 9 z + 4 z^2)) + 96 (-1 + y)^2 y (y^2 + 2 y (-1 \\&+ z) + 2 (-1 + z)^2) (-1 + z)^2 z (-1 + y + z) (y+ z)^2 (-1 + 4 z) H(2, y)) - 192 (-1 + y)^2 y (y^2 + 2 y (-1 + z) \\&+ 2 (-1 + z)^2) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-1+ 4 z) H(2, 2, y)) + H(2, y) (-96 (-1 + y)^2 y (-1 \\&+ 4 y) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z) - 2 z+ z^2) H(0, 0, y) - 96 (-1 + y)^2 y (y^2\\&+ 2 y (-1 + z) + 2 (-1 + z)^2) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-1 + 4 z) H(0, 0, z)- 96 (-1 + y)^2 y (y^2 \\&+ 2 y (-1 + z) + 2 (-1 + z)^2) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-1 + 4 z) H(0, 1, z) + 96 (-1 + y)^2 y (-1\\&+ 4 y) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z) - 2 z + z^2) H(0, 2, y) - 96 (-1 + y)^2 y (-1 \\&+ 4 y) (-1+ z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z) - 2 z + z^2) H(1, 0, y) - 96 (-1 + y)^2 y (y^2 \\&+ 2 y (-1 + z) + 2 (-1+ z)^2) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-1 + 4 z) H(1, 0, z) + 120 (-1 + y)^2 y (-1 \\&+ z)^2 z (-1 + y + z) (y + z)^2 (-4 + 56 y^3+ 50 z - 109 z^2 + 56 z^3 + y^2 (-109 + 84 z) + y (50 - 92 z \\&+ 84 z^2)) H(1, 1, z) + 96 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 + y+ z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z) - 2 z \\&+ z^2) H(2, 0, y) - 96 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-4 + 8 y^3+ 14 z - 19 z^2 + 8 z^3 + y^2 (-19 \\&+ 12 z)+ 2 y (7 - 10 z + 6 z^2)) H(2, 2, y) - 96 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y+ z)^2 (-4 + 8 y^3 + 14 z \\&- 19 z^2 + 8 z^3 + y^2 (-19 + 12 z) + 2 y (7 - 10 z + 6 z^2)) H(3, 2, y)) + H(1, z) (-60 (-1 + y)^2 y (-1+ z)^2 z (-1\\&+ y + z) (y + z)^2 (-4 + 56 y^3 + 50 z - 109 z^2 + 56 z^3 + y^2 (-109 + 84 z) + y (50 - 92 z + 84 z^2)) H(2, y)^2 \end{aligned}$$
$$\begin{aligned}&- 96 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-4 + 8 y^3 + 14 z - 19 z^2 + 8 z^3 + y^2 (-19 + 12 z) + 2 y (7 \\&- 10 z+ 6 z^2)) H(2, y) H(3, y) - 96 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 \\&+ z) - 2 z+ z^2) H(0, 0, y) - 96 (-1 + y)^2 y (y^2 + 2 y (-1 + z) + 2 (-1 + z)^2) (-1 + z)^2 z (-1 + y + z) (y \\&+ z)^2 (-1 + 4 z) H(0, 0, z)- 96 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 \\&+ z) - 2 z + z^2) H(0, 1, z) - 96 (-1+ y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z) \\&- 2 z + z^2) H(0, 2, y) - 96 (-1 + y)^2 y (-1+ z)^2 z (-1 + y + z) (y + z)^2 (-4 + 8 y^3 + 14 z - 19 z^2 + 8 z^3 \\&+ y^2 (-19 + 12 z) + 2 y (7 - 10 z + 6 z^2)) H(1, 1, z) - 96 (-1+ y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 + y + z)\\&\times (y + z)^2 (2 + 2 y^2+ 2 y (-2 + z) - 2 z + z^2) H(2, 0, y) + 120 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z)\\&\times (y + z)^2 (-4 + 56 y^3 + 50 z - 109 z^2 + 56 z^3 + y^2 (-109 + 84 z) + y (50 - 92 z + 84 z^2)) H(2, 2, y)\\&+ 96 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-4 + 8 y^3 + 14 z - 19 z^2 + 8 z^3 + y^2 (-19 + 12 z)\\&+ 2 y (7 - 10 z + 6 z^2)) H(2, 3, y) + 96 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-4 + 8 y^3 + 14 z\\&- 19 z^2 + 8 z^3 + y^2 (-19 + 12 z) + 2 y (7 - 10 z + 6 z^2)) H(3, 2, y)) + 72 (-1 + y)^2 y (-1 + z)^2\\&\times z (-1 + y + z) (y + z)^2 (-44 + 528 y^3 + 66 z - 99 z^2 + 64 z^3 + y^2 (-829 + 412 z) + 2 y\\&\times (187 - 176 z + 58 z^2)) H(0, 0, 0, y) + 72 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-44 + 64 y^3\\&+ 374 z - 829 z^2 + 528 z^3 + y^2 (-99 + 116 z) + y (66 - 352 z + 412 z^2)) H(0, 0, 0, z) + 192 (-1 + y)^2\\&\times y (-1 + 4 y) (-1+ z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z) - 2 z + z^2) H(0, 1, 1, z)\\&- 192 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 +y+ z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z) - 2 z + z^2)\\&\times H(0, 2, 2, y) + 96 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z)\\&\times - 2 z + z^2) H(1, 0, 1, z) + 96 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 \end{aligned}$$
$$\begin{aligned}&+ 2 y (-2 + z) - 2 z + z^2) H(1, 0, 2, y) + 72 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-12 + 104 y^3\quad \quad \quad \\&\times + 102 z - 207 z^2 + 104 z^3 + 3 y^2 (-69 + 52 z) + 6 y (17 - 30 z + 26 z^2))H(1, 1, 1, z) + 96 (-1 + y)^2\\&\times y (-1 + 4 y) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z) - 2 z + z^2) H(1, 2, 0, y)\\&\times - 192 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z) - 2 z + z^2)\\&\times H(2, 0, 2, y) + 96 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z)\\&- 2 z + z^2) H(2, 1, 0, y) - 192 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2\\&+ 2 y (-2 + z) - 2 z + z^2) H(2, 2, 0, y) + 72 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-12 + 104 y^3\\&+ 102 z - 207 z^2 + 104 z^3 + 3 y^2 (-69 + 52 z) + 6 y (17 - 30 z + 26 z^2)) H(2, 2, 2, y) + 96 (-1 + y)^2\\&\times y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-4 + 8 y^3 + 14 z - 19 z^2 + 8 z^3 + y^2 (-19 + 12 z) + 2 y (7\\&- 10 z + 6 z^2)) H(2, 3, 2, y) + 192 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-4 + 8 y^3 + 14 z - 19 z^2 \\&+ 8 z^3 + y^2 (-19 + 12 z) + 2 y (7 - 10 z + 6 z^2)) H(3, 2, 2, y)\Bigg \}\Big /\Big (48 (-1 + y)^2 y^2 (-1\\&+ z)^2 z^2 (-1 + y + z) (y + z)^2\Big );\\ \mathcal {A}_{3;n_{f}^{2}}^{(2)}&= \Bigg \{4 (5 y^7 (-1 + 4 z) + y^6 (15 - 83 z + 80 z^2) - 5 z^4 (-2 + 4 z - 3 z^2 + z^3) + y^5 (-20 + 147 z - 273 z^2 + 140 z^3)\\&+ y z^3 (40 - 154 z + 147 z^2 - 83 z^3 + 20 z^4) + y^2 z^2 (60 - 254 z + 363 z^2 - 273 z^3 + 80 z^4)\\&+ y^3 z (40 - 254 z + 462 z^2 - 439 z^3 + 140 z^4) + y^4 (10 - 154 z + 363 z^2 - 439 z^3 + 160 z^4)) \\&- 9 (y + z)^4 (2 + y^2 (3 - 9 z) - 4 z + 3 z^2 - z^3 + y^3 (-1 + 4 z) + y (-4 + 12 z - 9 z^2 + 4 z^3)) H(0, y)\\&\times - 9 (y + z)^4 (2 + y^2 (3 - 9 z) - 4 z + 3 z^2 - z^3 + y^3 (-1 + 4 z) + y (-4 + 12 z - 9 z^2 + 4 z^3)) H(0, z)\\&+ 36 y z (-5 y^3 + 3 y^4 + y z^2 + y^2 (6 + z - 6 z^2) + z^2 (6 - 5 z + 3 z^2)) H(1, z) + 36 y z (-5 y^3 + 3 y^4\\&+ y z^2 + y^2 (6 + z - 6 z^2) + z^2 (6 - 5 z + 3 z^2)) H(2, y)\Bigg \}\Big /\Big (216 y z (-1 + y + z) (y + z)^4\Big );\\ \end{aligned}$$
$$\begin{aligned} \mathcal {A}_{3;C_{A}C_{F}}^{(2)}&= \Bigg \{-4 (-1 + y) y (-1 + z) z (y + z) ((-1 + z)^2 z (5450 - 5153 z + 2725 z^2) + y^5 (2725 - 10952 z + 7336 z^2)\\&+ y^4 (-10603 + 43407 z - 37764 z^2 + 4960 z^3) + y^3 (18481 - 86606 z + 117680 z^2 - 53624 z^3\\&+ 4960 z^4) + y (5450 - 38046 z + 86747 z^2 - 86606 z^3 + 43407 z^4 - 10952 z^5) + y^2 (-16053 \\&+ 86747 z - 157946 z^2 + 117680 z^3 - 37764 z^4 + 7336 z^5)) + 36 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 \\&\times (272 + 3128 y^4 - 470 z + 417 z^2 - 419 z^3 + 200 z^4 + y^3 (-8003 + 5572 z) + 3 y^2 (2355 - 3089 z\\&+ 936 z^2) + y (-2462 + 4440 z - 2739 z^2 + 772 z^3)) H(0, y)^3 + 36 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 \\&\times (272 + 200 y^4 - 2462 z + 7065 z^2 - 8003 z^3 + 3128 z^4 + y^3 (-419 + 772 z) + 3 y^2 (139 - 913 z\\&+ 936 z^2) + y (-470 + 4440 z - 9267 z^2 + 5572 z^3)) H(0, z)^3 + 36 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2\\&\times (60 + 1048 y^4 - 1190 z + 3387 z^2 - 3305 z^3 + 1048 z^4 + y^3 (-3305 + 2652 z) + y^2 (3387 - 5793 z\\&+ 3624 z^2) + y (-1190 + 3984 z - 5793 z^2 + 2652 z^3)) H(1, z)^3 + 9 (2592 y^{10} (-1 + z)^2\\&- 324 (-1 + z)^5 z^4 (-1 + 4 z) + 4 y^9 (-1 + z)^2 (-3375 + 1232 z) + y^8 (28620 - 84611 z + 64366 z^2\\&+ 10459 z^3 - 18996 z^4) + y (-1 + z)^2 z^3 (-10284 + 31286 z - 47769 z^2 + 47069 z^3 - 22936 z^4\\&+ 2592 z^5) - y^7 (31212 - 112231 z + 31885 z^2 + 231313 z^3 - 265795 z^4 + 83616 z^5)\\&+ y^6 (18036 - 61763 z - 163792 z^2 + 837127 z^3 - 1162130 z^4 + 669294 z^5 - 136448 z^6)\\&- y^2 (-1 + z)^2 z^2 (8364 - 92610 z + 217312 z^2 - 239107 z^3 + 137650 z^4 - 33236 z^5 + 1296 z^6) \\&- y^5 (4968 + 12031 z - 343845 z^2 + 1384321 z^3 - 2358789 z^4 + 1969504 z^5 - 787230 z^6\\&+ 119040 z^7) + y^4 (432 + 28202 z - 276976 z^2 + 1189366 z^3 - 2507872 z^4 + 2799861 z^5\\&- 1679342 z^6 + 504259 z^7 - 58092 z^8) + y^3 z (-8772 + 93570 z - 525300 z^2+ 1423618 z^3\\&- 2064667 z^4 + 1697887 z^5 - 784219 z^6 + 182395 z^7 - 14512 z^8)) H(2, y)^2 + 36 (-1 + y)^2\\&\times y (-1 + z)^2 z (y + z)^2 (60 + 1048 y^4 - 1190 z + 3387 z^2 - 3305 z^3 + 1048 z^4 + y^3 (-3305 + 2652 z) \end{aligned}$$
$$\begin{aligned}&+ y^2 (3387 - 5793 z + 3624 z^2) + y (-1190 + 3984 z - 5793 z^2 + 2652 z^3)) H(2, y)^3\\&+ H(0, z)^2 (9 (324 (-1 + z)^6 z^3 (-1 + 4 z) + 16 y^9 (-1 + z)^2 (162 + 73 z)+ y^8 (-13500 + 34093 z\\&- 26250 z^2 + 5391 z^3 + 1180 z^4) + y^7 (28620 - 106481 z + 143631 z^2 - 77501 z^3 + 5003 z^4 + 6728 z^5)\\&- 2 y (-1 + z)^2 z^2 (108 - 3068 z + 15065 z^2 - 37089 z^3 + 46088 z^4 - 22256 z^5 + 1296 z^6) \\&+ y^6 (-31212 + 163509 z - 312112 z^2 + 240300 z^3 - 456 z^4 - 105981 z^5 + 44124 z^6) + 2 y^2 (-1 + z)^2\\&\times z (270 - 1316 z - 14807 z^2 + 70951 z^3 - 142240 z^4 + 124888 z^5 - 36250 z^6 + 648 z^7) \\&+ y^5 (18036 - 132635 z + 331953 z^2 - 300344 z^3 - 147828 z^4 + 523715 z^5 - 390745 z^6 + 97848 z^7)\\&+ y^4 (-4968 + 54838 z - 176524 z^2 + 144129 z^3 + 393770 z^4 - 1110625 z^5 + 1146516 z^6 - 538862 z^7\\&+ 92640 z^8) + y^3 (432 - 9848 z + 42974 z^2 + 4423 z^3 - 410951 z^4 + 1156123 z^5 - 1515467 z^6\\&+ 1025284 z^7 - 326466 z^8 + 33496 z^9)) - 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (y^3 (-1 + 4 z)\\&+ 4 y (-1 + z)^2 (-1 + 4 z) + 3 y^2 (1 - 5 z + 4 z^2) + 2 (1 - 8 z + 18 z^2 - 17 z^3 + 6 z^4)) H(1, z)\\&- 1728 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (2 - 15 z + 33 z^2 - 30 z^3 + 10 z^4 + y^3 (-1 + 4 z)\\&+ 4 y (-1 + z)^2 (-1 + 4 z) + 3 y^2 (1 - 5 z + 4 z^2)) H(2, y)) + H(0, y)^2 (-9 (2592 y^{10} (-1 + z)^2\\&+ 324 (-1 + z)^5 z^3 (-1 + 4 z) - 4 y^9 (-1 + z)^2 (4023 + 4486 z) - 6 y^8 (-7020 + 5368 z + 21840 z^2\\&- 31731 z^3 + 11516 z^4) + y^7 (-59832 + 90672 z + 223220 z^2 - 565474 z^3 + 397382 z^4 - 85968 z^5) \end{aligned}$$
$$\begin{aligned}&- y (-1 + z)^2 z^2 (-216 + 6244 z - 21180 z^2 + 34761 z^3 - 27075 z^4 + 7648 z^5) + y^6 (49248 \\&- 151456 z - 105440 z^2 + 735113 z^3 - 850650 z^4 + 378865 z^5 - 56004 z^6) + y^2 (-1 + z)^2 z (-540\\&+ 1876 z + 30168 z^2 - 80106 z^3 + 101421 z^4 - 58502 z^5 + 11408 z^6) - y^5 (23004 - 128508 z\\&+ 71864 z^2 + 470215 z^3 - 932695 z^4 + 701645 z^5 - 235797 z^6 + 30272 z^7) + y^4 (5400 - 53988 z\\&+ 88836 z^2 + 166115 z^3 - 638606 z^4 + 766830 z^5 - 456762 z^6 + 139069 z^7 - 16732 z^8)\\&- y^3 (432 - 9956 z + 29272 z^2 + 57505 z^3 - 334959 z^4 + 576238 z^5 - 518670 z^6 + 256651 z^7\\&- 61569 z^8 + 5056 z^9)) - 432 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 \\&+ 2 y (-2 + z) - 2 z + z^2) H(0, z) - 1728 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (2 + 10 y^4 - 4 z + 3 z^2\\&- z^3 + 2 y^3 (-15 + 8 z) + 3 y^2 (11 - 12 z + 4 z^2) + y (-15 + 24 z - 15 z^2 + 4 z^3)) H(1, z) \\&- 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (2 + 12 y^4 - 4 z + 3 z^2 - z^3 \end{aligned}$$
$$\begin{aligned}&+ 2 y^3 (-17 + 8 z) + 12 y^2 (3 - 3 z + z^2) + y (-16 + 24 z - 15 z^2 + 4 z^3)) H(2, y)) + H(1, z)^2 (9 (2592 y^{10} (-1 \\&+ z)^2- 324 (-1 + z)^5 z^4 (-1 + 4 z) + 4 y^9 (-1 + z)^2 (-3375 + 1232 z) + y^8 (28620 - 84611 z + 64366 z^2\\&+ 10459 z^3 - 18996 z^4)+ y (-1 + z)^2 z^3 (-10284 + 31286 z - 47769 z^2 + 47069 z^3 - 22936 z^4 + 2592 z^5) \\&- y^7 (31212 - 112231 z + 31885 z^2+ 231313 z^3 - 265795 z^4 + 83616 z^5) + y^6 (18036 - 61763 z - 163792 z^2 \\&+ 837127 z^3 - 1162130 z^4 + 669294 z^5 - 136448 z^6)- y^2 (-1 + z)^2 z^2 (8364 - 92610 z + 217312 z^2 - 239107 z^3 \\&+ 137650 z^4 - 33236 z^5 + 1296 z^6) - y^5 (4968 + 12031 z - 343845 z^2 + 1384321 z^3 - 2358789 z^4 + 1969504 z^5 \\&- 787230 z^6 + 119040 z^7) + y^4 (432 + 28202 z - 276976 z^2 + 1189366 z^3 - 2507872 z^4 + 2799861 z^5\\&- 1679342 z^6 + 504259 z^7 - 58092 z^8) + y^3 z (-8772 + 93570 z - 525300 z^2 + 1423618 z^3 - 2064667 z^4 \\&+ 1697887 z^5 - 784219 z^6 + 182395 z^7 - 14512 z^8)) + 108 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (124 + 1240 y^4\\&- 1510 z + 4011 z^2 - 3865 z^3 + 1240 z^4 + y^3 (-3865 + 2972 z) + y^2 (4011 - 6609 z + 4008 z^2) + y (-1510 \\&+ 4752 z - 6609 z^2 + 2972 z^3)) H(2, y) + 1728 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (4 + 12 y^4 - 20 z + 39 z^2 - 35 z^3 \\&+ 12 z^4 + 5 y^3 (-7 + 4 z) + 3 y^2 (13 - 17 z + 8 z^2) + y (-20 + 48 z - 51 z^2 + 20 z^3)) H(3, y)) + 18 (2592 y^{10} (-1\\&+ z)^2 + 324 (-1 + z)^5 z^3 (-1 + 4 z)- 4 y^9 (-1 + z)^2 (4023 + 4486 z) - 6 y^8 (-7020 + 5368 z + 21840 z^2 \\&- 31731 z^3 + 11516 z^4) + y^7 (-59832 + 90672 z + 223220 z^2 - 565474 z^3 + 397382 z^4 - 85968 z^5) - y (-1 \\&+ z)^2 z^2 (-216 + 6244 z - 21180 z^2 + 34761 z^3 - 27075 z^4 + 7648 z^5) + y^6 (49248 - 151456 z - 105440 z^2\\&+ 735113 z^3 - 850650 z^4 + 378865 z^5 - 56004 z^6) + y^2 (-1 + z)^2 z (-540+ 1876 z + 30168 z^2 - 80106 z^3 \\&+ 101421 z^4 - 58502 z^5 + 11408 z^6) - y^5 (23004 - 128508 z + 71864 z^2 + 470215 z^3\\&- 932695 z^4 + 701645 z^5 - 235797 z^6 + 30272 z^7) + y^4 (5400 - 53988 z + 88836 z^2 + 166115 z^3 - 638606 z^4 \end{aligned}$$
$$\begin{aligned}&+ 766830 z^5 - 456762 z^6 + 139069 z^7 - 16732 z^8) - y^3 (432 - 9956 z + 29272 z^2 + 57505 z^3 - 334959 z^4 \\&+ 576238 z^5 - 518670 z^6 + 256651 z^7 - 61569 z^8 + 5056 z^9)) H(0, 0, y) - 18 (324 (-1 + z)^6 z^3 (-1 + 4 z)\\&+ 16 y^9 (-1 + z)^2 (162 + 73 z) + y^8 (-13500 + 34093 z - 26250 z^2 + 5391 z^3 + 1180 z^4) + y^7 (28620 - 106481 z \\&+ 143631 z^2 - 77501 z^3 + 5003 z^4 + 6728 z^5) - 2 y (-1 + z)^2 z^2 (108 - 3068 z + 15065 z^2 - 37089 z^3 + 46088 z^4 \\&- 22256 z^5 + 1296 z^6) + y^6 (-31212 + 163509 z - 312112 z^2 + 240300 z^3 - 456 z^4 - 105981 z^5 + 44124 z^6) \\&+ 2 y^2 (-1 + z)^2 z (270 - 1316 z - 14807 z^2 + 70951 z^3 - 142240 z^4 + 124888 z^5 - 36250 z^6 + 648 z^7) \!+\! y^5 (18036\\&- 132635 z + 331953 z^2 - 300344 z^3 - 147828 z^4 + 523715 z^5 - 390745 z^6+ 97848 z^7) + y^4 (-4968 + 54838 z \\&- 176524 z^2 + 144129 z^3 + 393770 z^4 - 1110625 z^5 + 1146516 z^6 - 538862 z^7 + 92640 z^8)+ y^3 (432 - 9848 z \\&+ 42974 z^2 + 4423 z^3 - 410951 z^4 + 1156123 z^5 - 1515467 z^6 + 1025284 z^7 - 326466 z^8 + 33496 z^9)) H(0, 0, z) \\&- 216 (-1 + y)^2 y z (88 y^6 (-1 + z)^2 - (-1 + z)^3 z^2 (14 - 14 z + 3 z^2) + y^5 (-278 + 828 z - 816 z^2+ 272 z^3) \\&- y (-1 + z)^2 z (-68 + 202 z - 114 z^2 - 61 z^3 + 60 z^4) + 2 y^4 (157 - 686 z + 1012 z^2 - 591 z^3 + 114 z^4)\\&- y^3 (138 - 984 z + 2141 z^2 - 1802 z^3 + 433 z^4 + 68 z^5) + y^2 (14 - 340 z + 1129 z^2 - 1351 z^3 + 427 z^4 + 293 z^5\\&- 172 z^6)) H(0, 1, z) + 216 y (-1 + z)^2 z (88 y^8 + y^7 (-470 + 456 z) + 2 y^6 (511 - 1064 z + 482 z^2) + z^2 (30 - 60 z \\&+ 49 z^2 - 19 z^3) + y^5 (-1156 + 4028 z - 3857 z^2 + 1036 z^3) + y z (20 - 342 z + 666 z^2 - 509 z^3 + 162 z^4)\\&+ y^4 (716 - 3888 z + 6107 z^2 - 3483 z^3 + 564 z^4) + y^2 (30 - 432 z + 1885 z^2 - 2545 z^3 + 1441 z^4 - 273 z^5)\\&+ y^3 (-230 + 1944 z - 4787 z^2+ 4380 z^3 - 1557 z^4 + 124 z^5)) H(0, 2, y) - 2376 (-1 + y)^2 y (-1 + 4 y) (-1 \\&+ z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2+ 2 y (-2 + z) - 2 z + z^2) H(1, 0, y) + 432 (-1 + y)^2 y z (-4 (-1 + z)^3 z^2 (1 \\&- z + z^2) + y^5 (-4 + 48 z - 87 z^2 + 40 z^3) + 4 y (-1 + z)^2 z (-3 - 5 z + 27 z^2 - 31 z^3 + 13 z^4) + y^4 (8 - 128 z \\&+ 407 z^2 - 465 z^3 + 172 z^4) + y^3 (-8 + 124 z - 552 z^2 + 1046 z^3 - 889 z^4 + 276 z^5) + y^2 (4 - 28 z + 244 z^2 \\&- 760 z^3 + 1079 z^4 - 735 z^5 + 196 z^6)) H(1, 0, z) - 18 (2592 y^{10} (-1 + z)^2 - 324 (-1 + z)^5 z^4 (-1 + 4 z) \\&+ 4 y^9 (-1 + z)^2 (-3375 + 1232 z) + y^8 (28620 - 84611 z + 64366 z^2+ 10459 z^3 - 18996 z^4) + y (-1 \end{aligned}$$
$$\begin{aligned}&+ z)^2 z^3 (-10284 + 31286 z - 47769 z^2 + 47069 z^3 - 22936 z^4 + 2592 z^5) - y^7 (31212- 112231 z + 31885 z^2 \\&+ 231313 z^3 - 265795 z^4 + 83616 z^5) + y^6 (18036 - 61763 z - 163792 z^2 + 837127 z^3 - 1162130 z^4\\&+ 669294 z^5 - 136448 z^6) - y^2 (-1 + z)^2 z^2 (8364 - 92610 z + 217312 z^2 - 239107 z^3 + 137650 z^4 - 33236 z^5 \\&+ 1296 z^6) - y^5 (4968 + 12031 z - 343845 z^2 + 1384321 z^3 - 2358789 z^4 + 1969504 z^5 - 787230 z^6 + 119040 z^7) \\&+ y^4 (432 + 28202 z- 276976 z^2 + 1189366 z^3 - 2507872 z^4 + 2799861 z^5 - 1679342 z^6 + 504259 z^7\\&- 58092 z^8) + y^3 z (-8772 + 93570 z- 525300 z^2 + 1423618 z^3 - 2064667 z^4 + 1697887 z^5 - 784219 z^6 \\&+182395 z^7 \!-\! 14512 z^8)) H(1, 1, z) + H(3, y) (-864 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y \!+\! z)^2 (-4 \!+\! 8 y^3 \!+\! 14 z \\&- 19 z^2 + 8 z^3 + y^2 (-19 + 12 z) + 2 y (7 - 10 z + 6 z^2)) H(0, 1, z) - 864 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y \\&+ z)^2 (-4 + 8 y^3 + 14 z - 19 z^2 + 8 z^3 + y^2 (-19 + 12 z) + 2 y (7 - 10 z + 6 z^2)) H(1, 0, z) - 3456 (-1 + y)^2 y (-1\\&+ z)^2 z (y + z)^2 (4 + 12 y^4 - 20 z + 39 z^2 - 35 z^3 + 12 z^4 + 5 y^3 (-7 + 4 z) + 3 y^2 (13 - 17 z + 8 z^2) + y (-20\\&+ 48 z - 51 z^2 + 20 z^3)) H(1, 1, z)) + 216 y (-1 + z)^2 z (88 y^8 + y^7 (-470 + 456 z) + 2 y^6 (511 - 1064 z + 482 z^2) \\&+ z^2 (30 - 60 z + 49 z^2 - 19 z^3) + y^5 (-1156 + 4028 z - 3857 z^2 + 1036 z^3) + y z (20 - 342 z + 666 z^2 - 509 z^3 \\&+ 162 z^4) + y^4 (716 - 3888 z + 6107 z^2 - 3483 z^3 + 564 z^4) + y^2 (30 - 432 z + 1885 z^2 - 2545 z^3 + 1441 z^4 \\&- 273 z^5) + y^3 (-230 + 1944 z - 4787 z^2 + 4380 z^3 - 1557 z^4 + 124 z^5)) H(2, 0, y) - 18 (2592 y^{10} (-1 + z)^2 \\&- 324 (-1 + z)^5 z^4 (-1 + 4 z) + 4 y^9 (-1 + z)^2 (-3375 + 1232 z) + y^8 (28620 - 84611 z + 64366 z^2 + 10459 z^3\\&- 18996 z^4) + y (-1 + z)^2 z^3 (-10284 + 31286 z - 47769 z^2 + 47069 z^3 - 22936 z^4 + 2592 z^5) - y^7 (31212\\&- 112231 z + 31885 z^2 + 231313 z^3 - 265795 z^4 + 83616 z^5) + y^6 (18036 - 61763 z - 163792 z^2 + 837127 z^3\\&- 1162130 z^4 \end{aligned}$$
$$\begin{aligned}&+ 669294 z^5 - 136448 z^6) - y^2 (-1 + z)^2 z^2 (8364 - 92610 z + 217312 z^2 - 239107 z^3 + 137650 z^4 - 33236 z^5\\&+ 1296 z^6)- y^5 (4968 + 12031 z - 343845 z^2 + 1384321 z^3 - 2358789 z^4 + 1969504 z^5 - 787230 z^6 + 119040 z^7)\\&+ y^4 (432 + 28202 z - 276976 z^2 + 1189366 z^3 - 2507872 z^4 + 2799861 z^5 - 1679342 z^6 + 504259 z^7 - 58092 z^8)\\&+ y^3 z (-8772 + 93570 z - 525300 z^2 + 1423618 z^3 - 2064667 z^4 + 1697887 z^5 - 784219 z^6 + 182395 z^7\\&- 14512 z^8)) H(2, 2, y) + H(0, z) (1188 (-1 + y)^2 y^2 z^2 (-1 + y + z) (y + z)^2 (-12 + 30 z - 26 z^2 + 8 z^3\\&+ 3 y (4 - 9 z + 4 z^2)) - 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (4 y^4 + (-1 + z)^3 (-1 + 4 z) + y^3 (-13 + 8 z) \\&+ 3 y^2 (5 - 7 z + 4 z^2) + y (-7 + 18 z - 21 z^2 + 8 z^3)) H(1, z)^2 + 2376 (-1 + y)^2 y (y^2 + 2 y (-1 + z) + 2 (-1 \\&+ z)^2) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-1 + 4 z) H(2, y) - 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (5 + 4 y^4 - 39 z \\&+ 87 z^2 - 81 z^3 + 28 z^4 + y^3 (-15 + 16 z) + 3 y^2 (7 - 17 z + 12 z^2) + y (-15 + 66 z - 93 z^2 + 40 z^3)) H(2, y)^2 \\&+ H(1, z) (-432 (-1 + y)^2 y z (-4 (-1 + z)^3 z^2 (1 - z + z^2) + y^5 (-4 + 48 z - 87 z^2 + 40 z^3) + 4 y (-1 + z)^2 z (-3\\&- 5 z + 27 z^2 - 31 z^3 + 13 z^4) + y^4 (8 - 128 z + 407 z^2 - 465 z^3 + 172 z^4) + y^3 (-8 + 124 z - 552 z^2 + 1046 z^3\\&- 889 z^4 + 276 z^5) + y^2 (4 - 28 z + 244 z^2 - 760 z^3 + 1079 z^4 - 735 z^5 + 196 z^6)) - 864 (-1 + y)^2 y (-1 + z)^2 z (y\\&+ z)^2 (2 - 28 z + 69 z^2 - 67 z^3 + 24 z^4 + y^3 (-1 + 4 z) + 3 y^2 (1 - 7 z + 8 z^2) + y (-4 + 36 z - 63 z^2 \\&+ 28 z^3)) H(2, y) + 864 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-4 + 8 y^3 + 14 z - 19 z^2 + 8 z^3 + y^2 (-19\\&+ 12 z) + 2 y (7 - 10 z + 6 z^2)) H(3, y)) + 864 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 \end{aligned}$$
$$\begin{aligned}&+ 2 y (-2 + z) - 2 z + z^2) H(0, 0, y) + 864 (-1 + y)^2 y (y^2 + 2 y (-1 + z) + 2 (-1 + z)^2) (-1 + z)^2 z (-1 + y \\&+ z) (y + z)^2 (-1 + 4 z) H(0, 0, z) + 864 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 \\&+ 2 y (-2 + z) - 2 z + z^2) H(0, 1, z) + 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (4 - 18 z + 33 z^2 - 27 z^3 + 8 z^4 \\&+ y^3 (-2 + 8 z) + 6 y^2 (1 - 4 z + 2 z^2) + y (-8 + 36 z - 45 z^2 + 20 z^3)) H(0, 2, y) + 864 (-1 + y)^2 y (-1 \\&+ z)^2 z (-1 + y + z) (y + z)^2 (-4 + 8 y^3 + 14 z - 19 z^2 + 8 z^3 + y^2 (-19 + 12 z) + 2 y (7 - 10 z + 6 z^2)) H(1, 1, z)\\&+ 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (4 - 18 z + 33 z^2 - 27 z^3 + 8 z^4 + y^3 (-2 + 8 z) + 6 y^2 (1 - 4 z + 2 z^2)\\&+ y (-8 + 36 z - 45 z^2 + 20 z^3)) H(2, 0, y) + 1728 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (5 + 4 y^4 - 39 z + 87 z^2 - 81 z^3 \\&+ 28 z^4 + y^3 (-15 + 16 z) + 3 y^2 (7 - 17 z + 12 z^2) + y (-15 + 66 z - 93 z^2 + 40 z^3)) H(2, 2, y)) - 2376 (-1 \\&+ y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-4 + 8 y^3 + 14 z - 19 z^2 + 8 z^3 + y^2 (-19 + 12 z) + 2 y (7 - 10 z \\&+ 6 z^2)) H(3, 2, y) + H(0, y) (1188 y^2 (-1 + z)^2 z^2 (-1 + y + z) (y + z)^2 (8 y^3 + y (30 - 27 z) + 12 (-1 + z)\\&+ 2 y^2 (-13 + 6 z)) - 432 (-1 + y)^2 y (y^2 + 2 y (-1 + z) + 2 (-1 + z)^2) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-1 \\&+ 4 z) H(0, z)^2 - 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (5 + 28 y^4 - 15 z + 21 z^2- 15 z^3 + 4 z^4 + y^3 (-81 + 40 z) \\&+ y^2 (87 - 93 z + 36 z^2) + y (-39 + 66 z - 51 z^2 + 16 z^3)) H(1, z)^2 - 432 y (-1 + z)^2 z (y^7 (-4 + 52 z) + 4 y^6 (4 \\&- 57 z + 49 z^2) - 4 z^2 (-1 + 2 z - 2 z^2 + z^3) + y^5 (-28 + 408 z - 735 z^2 + 276 z^3) + 4 y z (-3 - 7 z + 31 z^2 \\&- 32 z^3 + 12 z^4) + y^4 (28 - 360 z + 1079 z^2 - 889 z^3 + 172 z^4) + y^2 (4 + 4 z + 244 z^2 - 552 z^3\\&+ 407 z^4 - 87 z^5) + y^3 (-16 + 136 z - 760 z^2 + 1046 z^3 - 465 z^4 + 40 z^5)) H(2, y) - 864 (-1 + y)^2 \end{aligned}$$
$$\begin{aligned}&\times y (-1 + z)^2 z (y + z)^2 (4 y^4 + (-1 + z)^3 (-1 + 4 z) + y^3 (-13 + 8 z) + 3 y^2 (5 - 7 z + 4 z^2) + y (-7 + 18 z\\&- 21 z^2 + 8 z^3)) H(2, y)^2 + H(0, z) (-864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (4 + 8 y^4 - 8 z + 6 z^2 - 2 z^3\\&+ y^3 (-27 + 20 z) + 3 y^2 (11 - 15 z + 4 z^2) + 2 y (-9 + 18 z - 12 z^2 + 4 z^3)) H(1, z) - 864 (-1 + y)^2 y (-1 + z)^2\\&\times z (y + z)^2 (4 - 18 z + 33 z^2 - 27 z^3 + 8 z^4 + y^3 (-2 + 8 z) + 6 y^2 (1 - 4 z + 2 z^2) + y (-8 + 36 z - 45 z^2 + 20 z^3))\\&\times H(2, y)) + H(1, z) (2376 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2\\&+ 2 y (-2 + z) - 2 z +z^2) - 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (2 + 24 y^4 - 4 z + 3 z^2 - z^3 + y^3 (-67 + 28 z)\\&+ 3 y^2(23 - 21 z + 8 z^2) + y(-28 + 36 z - 21 z^2 + 4 z^3)) H(2, y) + 864 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z)\\&\times (y + z)^2 (-4 + 8 y^3+ 14 z - 19 z^2 + 8 z^3 + y^2 (-19 + 12 z) + 2 y (7 - 10 z + 6 z^2)) H(3, y))\\&\times + 864(-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z) - 2 z + z^2)\\&\times H(0, 0, y) + 864 (-1 + y)^2 y (y^2 + 2 y (-1 + z) + 2 (-1 + z)^2) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-1 + 4 z)\\&\times H(0, 0, z) + 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (4 + 8 y^4 - 8 z + 6 z^2 - 2 z^3 + y^3 (-27 + 20 z)\\&+ 3 y^2 (11 - 15 z + 4 z^2) + 2 y (-9 + 18 z - 12 z^2 + 4 z^3)) H(0, 1, z) - 864 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2\\&\times z(-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z) - 2 z + z^2) H(0, 2, y) + 864 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 \\&\times z (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z) - 2 z + z^2) H(1, 0, y) + 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2\\&\times (4 + 8 y^4 - 8 z + 6 z^2 - 2 z^3 + y^3 (-27 + 20 z) + 3 y^2 (11 - 15 z + 4 z^2) + 2 y (-9 + 18 z - 12 z^2 + 4z^3))\\&\times H(1, 0, z) + 1728 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (5 + 28 y^4 - 15 z + 21 z^2 - 15 z^3 + 4 z^4 + y^3 (-81 + 40 z)\\&+ y^2 (87 - 93 z + 36 z^2) + y (-39 + 66 z - 51 z^2 + 16 z^3)) H(1, 1, z) - 864 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 \\&\times z (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z) - 2 z + z^2) H(2, 0, y) + 864 (-1 + y)^2 y (-1\\&+ z)^2 z (-1 + y + z) (y + z)^2 (-4 + 8 y^3 + 14 z - 19 z^2 + 8 z^3 + y^2 (-19 + 12 z) + 2 y (7 - 10 z + 6 z^2)) H(2, 2, y)\\&+ 864 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-4 + 8 y^3 + 14 z - 19 z^2 + 8 z^3 + y^2 (-19 + 12 z)\\&+ 2 y (7 - 10 z + 6 z^2)) H(3, 2, y)) + H(1, z) (1188 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y^4 (-3 + 20 z)\\&- 3 z^2 (2 - 2 z + z^2) + y^3 (6 - 50 z + 60 z^2) + 2 y z (4 + 17 z - 25 z^2 + 10 z^3) + y^2 (-6 + 34 z - 94 z^2 + 60 z^3))\\&+ 108 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (124 + 1240 y^4 - 1510 z + 4011 z^2 - 3865 z^3 + 1240 z^4\\&+ y^3 (-3865 + 2972 z) + y^2 (4011 - 6609 z + 4008 z^2) + y (-1510 \end{aligned}$$
$$\begin{aligned}&+ 4752 z - 6609 z^2 + 2972 z^3)) H(2, y)^2 - 2376 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-4 + 8 y^3 \\&+ 14 z - 19 z^2 + 8 z^3 + y^2 (-19 + 12 z) + 2 y (7 - 10 z + 6 z^2)) H(3, y) + 1728 (-1 + y)^2 y (-1 + z)^2\\&\times z (y + z)^2 (4 +12 y^4 - 20 z + 39z^2 - 35 z^3 + 12 z^4 + 5 y^3 (-7 + 4 z) + 3y^2 (13 - 17 z + 8 z^2) \\&+y (-20 + 48 z - 51 z^2 + 20 z^3)) H(2, y) H(3, y) + 3456 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (2 + 10 y^4\\&- 4 z + 3 z^2 - z^3 +2 y^3 (-15 + 8 z) + 3 y^2 (11 - 12 z + 4 z^2) + y (-15 + 24 z - 15 z^2 + 4 z^3))\\&\times H(0, 0, y) + 864 (-1 +y)^2 y (-1 + z)^2 z (y +z)^2 (2 - 28 z + 69 z^2 - 67 z^3 + 24 z^4 + y^3 (-1 + 4 z)\\&+ 3 y^2 (1 - 7 z + 8 z^2) + y (-4 + 36 z -63 z^2 + 28 z^3)) H(0,0, z) + 1728 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2\\&\times (2 + 12 y^4 - 4 z + 3 z^2 - z^3 + 2 y^3 (-17 + 8 z) +12 y^2 (3 - 3 z + z^2) +y (-16 + 24 z - 15 z^2 + 4 z^3))\\&\times H(0, 1, z) + 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (2 + 24 y^4- 4 z + 3 z^2 - z^3 +y^3 (-67 + 28 z)\\&+ 3 y^2 (23 - 21 z + 8 z^2) + y (-28 + 36 z - 21 z^2 + 4 z^3)) H(0, 2, y) - 864 (-1 +y)^2 y (-1 + z)^2\\&\times z (-1+ y + z) (y + z)^2 (-4 + 8 y^3 + 14 z - 19 z^2 + 8 z^3 + y^2 (-19+ 12 z) + 2 y (7 - 10 z + 6 z^2))\\&\times H(0, 3,y) - 864 (-1 + y)^2 y(-1 + z)^2 z (y + z)^2 (2 + y^2 (3 - 9 z) - 4 z + 3 z^2 - z^3 + y^3 (-1 + 4 z)\\&+ y (-4 + 12 z - 9 z^2 + 4z^3)) H(1, 0, z) + 1728 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (4 + 12y^4 - 20 z + 39z^2- 35 z^3 \\&+ 12 z^4 + 5 y^3 (-7 + 4 z) + 3y^2 (13 - 17 z + 8 z^2) +y (-20 + 48 z - 51 z^2 + 20 z^3)) H(1, 1, z)+ 864 (-1 + y)^2\\&\times y (-1 + z)^2 z (y \!+\! z)^2 (2 + 24 y^4- 4 z + 3 z^2 - z^3 +y^3 (-67 + 28 z) + 3 y^2 (23 \!-\! 21 z \!+\! 8 z^2)+ y (-28 \!+\! 36 z \!-\! 21 z^2\\&+ 4 z^3)) H(2, 0, y) - 216 (-1 +y)^2 y (-1 + z)^2 z (y +z)^2 (124 + 1240 y^4 - 1510 z+ 4011 z^2 - 3865 z^3 + 1240 z^4 \end{aligned}$$
$$\begin{aligned}&+ y^3 (-3865 + 2972 z) + y^2 (4011 - 6609 z + 4008 z^2) + y (-1510+ 4752 z - 6609 z^2 + 2972 z^3)) H(2, 2, y)\\&- 1728 (-1+ y)^2 y (-1 + z)^2 z (y + z)^2 (4 + 12 y^4 - 20 z + 39 z^2 - 35z^3 + 12 z^4 + 5 y^3 (-7 + 4 z)\\&+ 3 y^2 (13 - 17 z + 8 z^2) + y (-20 + 48 z - 51 z^2 + 20 z^3)) H(2, 3, y) - 864 (-1 + y)^2 y(-1 + z)^2\\&\times z (-1 + y + z) (y + z)^2 (-4 + 8 y^3 + 14 z - 19 z^2 + 8 z^3 + y^2 (-19 + 12 z) + 2 y (7 - 10 z + 6 z^2))\\&\times H(3, 0, y) -1728 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (4 + 12 y^4 - 20 z + 39 z^2 - 35 z^3 + 12 z^4+ 5 y^3 (-7 + 4 z)\\&+ 3 y^2 (13 - 17 z +8 z^2) + y (-20 + 48 z - 51 z^2 + 20 z^3)) H(3, 2, y)) + H(2, y) (1188 (-1 + y)^2\\&\times y (-1 + z)^2 z (-1 + y + z) (y^4 (-3 +20 z) - 3 z^2 (2 - 2 z + z^2) + y^3 (6 - 50 z + 60 z^2)\\&+ 2 y z (4 + 17 z - 25 z^2 + 10 z^3) + y^2 (-6 + 34 z - 94 z^2 +60 z^3)) + 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2\\&\times (2 + 24 y^4 - 4 z + 3 z^2 - z^3 + y^3 (-67 + 28 z) + 3 y^2 (23 - 21 z + 8 z^2)+ y (-28 + 36 z - 21 z^2 + 4 z^3)) \\&\times H(0, 0, y) + 3456 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (2 - 15 z + 33 z^2 - 30 z^3 + 10 z^4 + y^3 (-1 + 4 z)\\&\times + 4 y (-1 + z)^2 (-1 + 4 z) + 3 y^2 (1 - 5 z + 4 z^2))H(0, 0, z) + 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2\\&\times (2- 28 z + 69 z^2 - 67 z^3 + 24 z^4 + y^3 (-1 + 4 z) + 3 y^2 (1 - 7 z + 8 z^2)+ y (-4 + 36 z - 63 z^2 + 28 z^3))\\&\times H(0, 1, z) - 1728 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (2 + 12 y^4 - 4 z + 3 z^2 - z^3 + 2 y^3 (-17 + 8 z)\\&+ 12 y^2 (3 - 3 z + z^2) + y (-16 + 24z - 15 z^2 + 4 z^3)) H(0, 2, y) + 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2\\&\times (2 + 24 y^4 - 4 z + 3 z^2 - z^3 + y^3 (-67 + 28z) + 3 y^2 (23 - 21 z + 8 z^2) + y (-28 + 36 z - 21 z^2 + 4 z^3))\\&\times H(1, 0, y) + 864 (-1 + y)^2 y (-1 + z)^2z (y + z)^2 (2 - 28 z + 69 z^2 - 67 z^3 + 24 z^4 + y^3 (-1 + 4 z) \\&+ 3 y^2 (1 - 7 z + 8 z^2) + y (-4 + 36 z - 63 z^2 + 28 z^3)) H(1, 0, z) -216 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2\\&\times (124 + 1240 y^4 - 1510 z + 4011 z^2 - 3865 z^3 + 1240 z^4 + y^3 (-3865 + 2972 z) + y^2 (4011 - 6609 z + 4008 z^2)\\&+ y (-1510 + 4752 z - 6609 z^2 + 2972 z^3)) H(1, 1, z) - 1728 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (2 + 12 y^4\\&\times - 4 z + 3 z^2 - z^3 + 2 y^3 (-17 + 8 z) + 12 y^2 (3 - 3 z + z^2) + y (-16 + 24 z - 15 z^2 + 4 z^3)) H(2, 0, y)\\&+ 1728 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (4 + 12 y^4 - 20 z + 39 z^2 - 35 z^3 + 12 z^4 + 5 y^3 (-7 + 4 z) + 3 y^2\\&\times (13 - 17 z + 8 z^2) + y (-20 + 48 z - 51 z^2 + 20 z^3)) H(2, 2, y) + 1728 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2\\&\times (4 + 12 y^4 - 20 z + 39 z^2 - 35 z^3 + 12 z^4 + 5 y^3 (-7 + 4 z) + 3 y^2 (13 - 17 z + 8 z^2) \\&+ y (-20 + 48 z - 51 z^2 + 20 z^3)) H(3, 2, y)) - 216 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (296 + 3224 y^4 - 518 z\\&+ 453 z^2 - 431 z^3 + 200 z^4 + y^3 (-8315 + 5764 z) + 3 y^2 (2475 - 3233 z + 984 z^2) + y (-2630 + 4728 z\\&- 2919 z^2 + 820 z^3)) H(0, 0, 0, y) - 216 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (296 + 200 y^4 - 2630 z + 7425 z^2\\&- 8315 z^3 + 3224 z^4 + y^3 (-431 + 820 z) + 3 y^2 (151 - 973 z + 984 z^2) + y (-518 + 4728 z - 9699 z^2 + 5764 z^3))\\&\times H(0, 0, 0, z) - 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (2 + 16 y^4 - 4 z + 3 z^2 - z^3 + y^3 (-51 + 28 z)\\&+ 3 y^2 (19 - 21 z + 8 z^2) + y (-24 + 36 z - 21 z^2 + 4 z^3)) H(0, 0, 1, z) + 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2\\&\times (16 y^4 + y^3 (-53 + 36 z) + 3 y^2 (21 - 27 z + 8 z^2) - 3 (-2 + 4 z - 3 z^2 + z^3) + y (-32 + 60 z - 39 z^2 + 12 z^3))\\&\times H(0, 0, 2, y) - 864 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2 z (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z)\\&\times - 2 z + z^2) H(0, 1, 0, y) - 864 (-1 + y)^2 y^2 (-1 + z)^2 z (y + z)^2 (8 y^3 + y^2 (-25 + 12 z)\\&\times - 2 (5 - 6 z + 3 z^2) + 3 y (9 - 9 z + 4 z^2)) H(0, 1, 0, z) - 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (48 y^4 \\&\times + y^3 (-137 + 68 z) + 3 y^2 (49 - 51 z + 16 z^2) - 5 (-2 + 4 z - 3 z^2 + z^3) + y (-68 + 108 z - 69 z^2 + 20 z^3))\\&\times H(0, 1, 1, z) + 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (16 y^4 + y^3 (-53 + 36 z) + 3 y^2 (21 - 27 z + 8 z^2)\\&\times - 3 (-2 + 4 z - 3 z^2 + z^3) + y (-32 + 60 z - 39 z^2 + 12 z^3)) H(0, 2, 0, y) + 2592 (-1 + y)^2 y (-1 + z)^2\\&\times z (y + z)^2 (2 + 16 y^4 - 4 z + 3 z^2 - z^3 + 5 y^3 (-9 + 4 z) + y^2 (47 - 45 z + 16 z^2) + y (-20 + 28 z - 17 z^2 + 4 z^3))\\&\times H(0, 2, 2, y) - 864 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-4 + 8 y^3 + 14 z - 19 z^2 + 8 z^3\\&+ y^2 (-19 + 12 z) + 2 y (7 - 10 z + 6 z^2)) H(0, 3, 2, y) - 1728 (-1 + y)^2 y (-1 + 4 y) (-1 + z)^2\\&\times z (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z) - 2 z + z^2) H(1, 0, 0, y) + 864 (-1 + y)^2 y (-1 + z)^2\\&\times z (y + z)^2 (2 + y^2 (3 - 9 z) - 4 z + 3 z^2 - z^3 + y^3 (-1 + 4 z) + y (-4 + 12 z - 9 z^2 + 4 z^3)) H(1, 0, 0, z) \end{aligned}$$
$$\begin{aligned}&\times - 1728 (-1+ y)^2 y (-1 + z)^2 z (y + z)^2 (2 + 12 y^4 - 4 z + 3 z^2 - z^3 + 2 y^3 (-17 + 8 z) + 12 y^2 (3 - 3 z + z^2) \\&+ y (-16 + 24 z - 15 z^2 + 4 z^3)) H(1, 0, 1, z) - 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (2 + 24 y^4 - 4 z + 3 z^2 - z^3 \\&+ y^3 (-67 + 28 z) + 3 y^2 (23 - 21 z + 8 z^2) + y (-28 + 36 z - 21 z^2 + 4 z^3)) H(1, 0, 2, y) + 864 (-1 + y)^2\\&\times y (-1 + z)^2 z (y + z)^2 (2 + y^2 (3 - 9 z) - 4 z + 3 z^2 - z^3 + y^3 (-1 + 4 z) + y (-4 + 12 z - 9 z^2 + 4 z^3))\\&\times H(1, 1, 0, z) - 216 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (156 + 1336 y^4 - 1670 z + 4323 z^2 - 4145 z^3 + 1336 z^4\\&\times + y^3 (-4145 + 3132 z) + y^2 (4323 - 7017 z + 4200 z^2) + y (-1670 + 5136 z - 7017 z^2 + 3132 z^3)) H(1, 1, 1, z)\\&\times - 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (2 + 24 y^4 - 4 z + 3 z^2 - z^3 + y^3 (-67 + 28 z) + 3 y^2 (23 - 21 z + 8 z^2)\\&\times + y (-28 + 36 z - 21 z^2 + 4 z^3)) H(1, 2, 0, y) + 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (16 y^4 + y^3 (-53 + 36 z)\\&\times + 3 y^2 (21 - 27 z + 8 z^2) - 3 (-2 + 4 z - 3 z^2 + z^3) + y (-32 + 60 z - 39 z^2 + 12 z^3)) H(2, 0, 0, y)\\&\times + 2592 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (2 + 16 y^4 - 4 z + 3 z^2 - z^3 + 5 y^3 (-9 + 4 z) + y^2 (47 - 45 z + 16 z^2)\\&\times + y (-20 + 28 z - 17 z^2 + 4 z^3)) H(2, 0, 2, y) - 864 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (2 + 24 y^4 - 4 z + 3 z^2 - z^3\\&\times + y^3 (-67 + 28 z) + 3 y^2 (23 - 21 z + 8 z^2) + y (-28 + 36 z - 21 z^2 + 4 z^3)) H(2, 1, 0, y) + 2592 (-1 + y)^2 y\\&\times (-1 + z)^2 z (y + z)^2 (2 + 16 y^4 - 4 z + 3 z^2 - z^3 + 5 y^3 (-9 + 4 z) + y^2 (47 - 45 z + 16 z^2) + y (-20 + 28 z\\&- 17 z^2 + 4 z^3)) H(2, 2, 0, y) - 216 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (156 + 1336 y^4 - 1670 z + 4323 z^2- 4145 z^3\\&+ 1336 z^4 + y^3 (-4145 + 3132 z) + y^2 (4323 - 7017 z + 4200 z^2)+ y (-1670 + 5136 z - 7017 z^2 + 3132 z^3)) \end{aligned}$$
$$\begin{aligned}&\quad \times H(2, 2, 2, y)- 1728 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2 (4 + 12 y^4 - 20 z + 39 z^2 - 35 z^3 + 12 z^4 + 5 y^3 (-7 + 4 z)\\&+ 3 y^2 (13 - 17 z + 8 z^2) + y (-20 + 48 z - 51 z^2 + 20 z^3)) H(2, 3, 2, y) - 864 (-1 + y)^2 y (-1 + z)^2\\&\times z (-1 + y + z) (y + z)^2 (-4 + 8 y^3 + 14 z - 19 z^2 + 8 z^3 + y^2 (-19 + 12 z) + 2 y (7 - 10 z + 6 z^2))\\&\times H(3, 0, 2, y) - 864 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (-4 + 8 y^3 + 14 z - 19 z^2 + 8 z^3\\&+ y^2 (-19 + 12 z) + 2 y (7 - 10 z + 6 z^2)) H(3, 2, 0, y) - 3456 (-1 + y)^2 y (-1 + z)^2 z (y + z)^2\\&\times (4 + 12 y^4 - 20 z + 39 z^2 - 35 z^3 + 12 z^4 + 5 y^3 (-7 + 4 z) + 3 y^2 (13 - 17 z + 8 z^2) + y (-20 + 48 z\\&\quad - 51 z^2 + 20 z^3)) H(3, 2, 2, y)\Bigg \}\Big / \Big (864 (-1 + y)^2 y^2 (-1 + z)^2 z^2 (-1 + y + z) (y + z)^2\Big );\\ \mathcal {A}_{3;C_{A}n_{f}}^{(2)}&= \Bigg \{-8 (-1 + y) (-1 + z) (y + z) (103 y^6 (-1 + 4 z) + 6 y^5 (47 - 272 z + 170 z^2) + z^3 (206 - 385 z + 282 z^2\\&- 103 z^3) + y^4 (-385 + 2703 z - 4017 z^2 + 1000 z^3) + 3 y^2 z (206 - 1022 z + 1843 z^2 - 1339 z^3 + 340 z^4)\\&+ y z^2 (618 - 2620 z + 2703 z^2 - 1632 z^3 + 412 z^4) + y^3 (206 - 2620 z + 5529 z^2 - 4976 z^3 + 1000 z^4)) \\&+ 9 (-1 + y) (-1 + z) (y + z)^4 (-56 + 72 y^4 + 529 z - 1569 z^2 + 1834 z^3 - 744 z^4 - 4 y^3 (31 + 12 z)\\&- 3 y^2 (5 - 182 z + 216 z^2) + y (105 - 1020 z + 2160 z^2 - 1336 z^3)) H(0, y)^2 - 216 (-1 + y) (-1 + z)\\&\times z (-1 + y + z) (y + z)^4 (3 - 12 z + 10 z^2 + y (-3 + 6 z)) H(0, y)^3 - 9 (-1 + y) (-1 + z) (y + z)^4 (56 + 744 y^4\\&- 105 z + 15 z^2 + 124 z^3 - 72 z^4 + 2 y^3 (-917 + 668 z) + 3 y^2 (523 - 720 z + 216 z^2) + y (-529 + 1020 z\\&- 546 z^2 + 48 z^3)) H(0, z)^2 - 216 (-1 + y) y (3 + 10 y^2 + 6 y (-2 + z) - 3 z) (-1 + z) (-1 + y + z) (y + z)^4\\&\times H(0, z)^3 + 1080 (-1 + y) (-1 + z) (-1 + y + z) (y + z)^4 (10 y^3 + 6 y^2 (-2 + z) + y (3 - 6 z + 6 z^2)\\&+ z (3 - 12 z + 10 z^2)) H(1, z)^3 - 72 (-1 + y) (-1 + z) (358 y^8 + 14 y^7 (-63 + 152 z)\\&+ y^6 (732 - 4821 z + 5640 z^2) + y^5 (-223 + 3798 z - 11757 z^2 + 9136 z^3) + z^4 (14 - 223 z + 732 z^2 - 882 z^3 \\&+ 358 z^4) + y z^3 (128 - 1175 z + 3798 z^2 - 4821 z^3 + 2128 z^4) + 2 y^3 z (64 - 1109 z + 5394 z^2 - 8670 z^3\\&+ 4568 z^4) + y^2 z^2 (84 - 2218 z + 8460 z^2 - 11757 z^3 + 5640 z^4) + y^4 (14 - 1175 z + 8460 z^2 - 17340 z^3\\&+ 10532 z^4)) H(2, y)^2 + 1080 (-1 + y) (-1 + z) (-1 + y + z) (y + z)^4 (10 y^3 + 6 y^2 (-2 + z) \\&+ y (3 - 6 z + 6 z^2) + z (3 - 12 z + 10 z^2)) H(2, y)^3 + H(0, y) (18 (-1 + z) (y + z)^4 (y^4 (-31 + 220 z)\\&+ y^3 (124 - 607 z + 96 z^2) + 31 (-2 + 4 z - 3 z^2 + z^3) - 31 y (-6 + 16 z - 12 z^2 + 5 z^3) \\&+ y^2 (-217 + 759 z - 387 z^2 + 124 z^3)) + 216 (-1 + y) (-1 + z) (y + z)^4 (2 + y^2 (3 - 9 z) - 4 z + 3 z^2\\&- z^3 + y^3 (-1 + 4 z) + y (-4 + 12 z - 9 z^2 + 4 z^3)) H(0, z) + 216 (-1 + y) (-1 + z) (y + z)^4 (2 + 16 y^4 - 4 z\\&+ 3 z^2 - z^3 + 2 y^3 (-21 + 8 z) + 6 y^2 (7 - 6 z + 2 z^2) + y (-18 + 24 z - 15 z^2 + 4 z^3)) H(1, z) + 288 (-1 + y)\\&\times y (-1 + z) z (-5 y^3 + 3 y^4 + y z^2 + y^2 (6 + z - 6 z^2) + z^2 (6 - 5 z + 3 z^2)) H(2, y)) + H(1, z)^2 (-72 (-1 + y)\\&\times (-1 + z) (358 y^8 + 14 y^7 (-63 + 152 z) + y^6 (732 - 4821 z + 5640 z^2) + y^5 (-223 + 3798 z - 11757 z^2\\&+ 9136 z^3) + z^4 (14 - 223 z + 732 z^2 - 882 z^3 + 358 z^4) + y z^3 (128 - 1175 z + 3798 z^2 - 4821 z^3 + 2128 z^4)\\&+ 2 y^3 z (64 - 1109 z + 5394 z^2 - 8670 z^3 + 4568 z^4) + y^2 z^2 (84 - 2218 z + 8460 z^2 - 11757 z^3 + 5640 z^4)\\&+ y^4 (14 - 1175 z + 8460 z^2 - 17340 z^3 + 10532 z^4)) + 3240 (-1 + y) (-1 + z) (-1 + y + z) (y + z)^4 (10 y^3 \\&+ 6 y^2 (-2 + z) + y (3 - 6 z + 6 z^2) + z (3 - 12 z + 10 z^2)) H(2, y)) + H(0, z) (18 (-1 + y) (y + z)^4\\&\times (-31 (-1 + z)^2 (2 - 2 z + z^2) + 31 y^3 (1 - 5 z + 4 z^2) + y^2 (-93 + 372 z - 387 z^2 + 96 z^3)\\&+ y (124 - 496 z + 759 z^2 - 607 z^3 + 220 z^4)) + 288 (-1 + y) y (-1 + z) z (-5 y^3 + 3 y^4 \\&+ y z^2 + y^2 (6 + z - 6 z^2) + z^2 (6 - 5 z + 3 z^2)) H(1, z) + 216 (-1 + y) (-1 + z) (y + z)^4 \\&\times (y^3 (-1 + 4 z) + 4 y (-1 + z)^2 (-1 + 4 z) + 3 y^2 (1 - 5 z + 4 z^2) + 2 (1 - 9 z + 21 z^2 - 21 z^3\\&+ 8 z^4)) H(2, y)) - 18 (-1 + y) (-1 + z) (y + z)^4 (-56 + 72 y^4 + 529 z - 1569 z^2 + 1834 z^3 - 744 z^4\\&\times - 4 y^3 (31 + 12 z) - 3 y^2 (5 - 182 z + 216 z^2) + y (105 - 1020 z + 2160 z^2 - 1336 z^3)) H(0, 0, y)\\&\times + 18 (-1 + y) (-1 + z) (y + z)^4 (56 + 744 y^4 - 105 z + 15 z^2 + 124 z^3 - 72 z^4 + 2 y^3 (-917 + 668 z)\\&\times + 3 y^2 (523 - 720 z + 216 z^2) + y (-529 + 1020 z - 546 z^2 + 48 z^3)) H(0, 0, z) - 72 (-1 + y) (-1 + z)\\&\times (48 y^8 + 6 y^7 (-21 + 40 z) + 6 y^6 (21 - 102 z + 86 z^2) - 3 z^4 (-2 + 4 z - 3 z^2 \end{aligned}$$
$$\begin{aligned}&+ z^3) + 3 y^5 (-18 + 196 z - 411 z^2 + 212 z^3) + y z^3 (48 - 122 z + 120 z^2 - 57 z^3 + 12 z^4)\\&+ 2 y^2 z^2 (18 - 142 z + 234 z^2 - 153 z^3 + 42 z^4) + 4 y^3 z (12 - 92 z + 237 z^2 - 210 z^3\\&+ 66 z^4) + y^4 (6 - 248 z + 1053 z^2 - 1335 z^3 + 504 z^4)) H(0, 1, z) + 72 (-1 + y) (-1 + z)\\&\times (48 y^8 + 6 y^7 (-21 + 40 z) + 6 y^6 (21 - 102 z + 86 z^2) - 3 z^4 (-2 + 4 z - 3 z^2 + z^3) + y z^4 (-82 + 96 z - 57 z^2\\&+ 12 z^3) + 4 y^3 z^2 (-94 + 249 z - 210 z^2 + 66 z^3) + 3 y^5 (-18 + 188 z - 411 z^2 + 212 z^3) + 2 y^2 z^2 (18 - 146 z\\&+ 234 z^2 - 153 z^3 + 42 z^4) + y^4 (6 - 208 z + 1053 z^2 - 1335 z^3 + 504 z^4)) H(0, 2, y) - 216 (-1 + y) y (-1 + z)\\&\times (y + z)^4 (16 y^3 + y^2 (-41 + 12 z) - 2 (7 - 6 z + 3 z^2) + 3 y (13 - 9 z + 4 z^2)) H(1, 0, y) \\&+ 72 (-1 + y) (-1 + z) (3 y^7 (-1 + 4 z) + y^6 (9 - 39 z + 48 z^2) - 3 z^4 (-2 + 4 z - 3 z^2 + z^3)\\&+ y z^4 (-40 + 60 z - 39 z^2 + 12 z^3) + 3 y^5 (-4 + 20 z - 51 z^2 + 28 z^3) + y^3 z^2 (-124 + 312 z - 285 z^2 + 84 z^3)\\&+ y^2 z^2 (36 - 124 z + 207 z^2 - 153 z^3 + 48 z^4) + y^4 (6 - 40 z + 207 z^2 - 285 z^3 + 96 z^4)) H(1, 0, z)\\&+ 144 (-1 + y) (-1 + z) (358 y^8 + 14 y^7 (-63 + 152 z) + y^6 (732 - 4821 z + 5640 z^2) + y^5 (-223\\&+ 3798 z - 11757 z^2 + 9136 z^3) + z^4 (14 - 223 z + 732 z^2 - 882 z^3 + 358 z^4) + y z^3 (128 - 1175 z + 3798 z^2\\&- 4821 z^3 + 2128 z^4) + 2 y^3 z (64 - 1109 z + 5394 z^2 - 8670 z^3 + 4568 z^4) + y^2 z^2 (84 - 2218 z + 8460 z^2\\&- 11757 z^3 + 5640 z^4) + y^4 (14 - 1175 z + 8460 z^2 - 17340 z^3 + 10532 z^4)) H(1, 1, z) + H(2, y) (36 (-1 + y)\\&\times (-1 + z) (y^7 (-9 + 84 z) + 3 y^6 (9 - 83 z + 144 z^2) - 9 z^4 (-2 + 4 z - 3 z^2 + z^3) + 3 y^5 (-12 + 70 z - 373 z^2\\&+ 324 z^3) + y z^3 (-168 - 26 z + 210 z^2 - 249 z^3 + 84 z^4) + y^2 z^2 (-60 - 314 z + 1053 z^2 - 1119 z^3 + 432 z^4)\\&+ y^3 z (-168 - 314 z + 1740 z^2 - 2175 z^3 + 972 z^4) + y^4 (18 - 26 z + 1053 z^2 - 2175 z^3 + 1248 z^4)) \end{aligned}$$
$$\begin{aligned}&- 6480 (-1 + y) (-1 + z) (-1 + y + z) (y + z)^4 (10 y^3 + 6 y^2 (-2 + z)\\&+ y (3 - 6 z + 6 z^2) + z (3 - 12 z + 10 z^2)) H(1, 1, z)) + 72 (-1 + y) (-1 + z) (48 y^8 + 6 y^7 (-21 + 40 z) \\&+ 6 y^6 (21 - 102 z + 86 z^2)- 3 z^4 (-2 + 4 z - 3 z^2 + z^3) + y z^4 (-82 + 96 z - 57 z^2 + 12 z^3)\\&+ 4 y^3 z^2 (-94 + 249 z - 210 z^2 + 66 z^3) + 3 y^5 (-18 + 188 z - 411 z^2 + 212 z^3) \\&+ 2 y^2 z^2 (18 - 146 z + 234 z^2 - 153 z^3 + 42 z^4) + y^4 (6 - 208 z + 1053 z^2 - 1335 z^3+ 504 z^4))\\&\times H(2, 0, y) + 144 (-1 + y) (-1 + z) (358 y^8 + 14 y^7 (-63 + 152 z) + y^6 (732 - 4821 z + 5640 z^2)\\&+ y^5 (-223 + 3798 z - 11757 z^2 + 9136 z^3) + z^4 (14 - 223 z + 732 z^2 - 882 z^3 + 358 z^4)\\&+ y z^3 (128 - 1175 z + 3798 z^2 - 4821 z^3 + 2128 z^4) + 2 y^3 z (64 - 1109 z + 5394 z^2 - 8670 z^3\\&+ 4568 z^4) + y^2 z^2 (84 - 2218 z + 8460 z^2 - 11757 z^3 + 5640 z^4) + y^4 (14 - 1175 z + 8460 z^2\\&- 17340 z^3 + 10532 z^4)) H(2, 2, y) + H(1, z) (36 (-1 + y) (-1 + z) (y^7 (-9 + 84 z) + 3 y^6 (9 - 83 z + 144 z^2)\\&- 9 z^4 (-2 + 4 z - 3 z^2 + z^3) + 3 y^5 (-12 + 70 z - 373 z^2 + 324 z^3) + y z^3 (-168 - 26 z + 210 z^2 \\&- 249 z^3 + 84 z^4) + y^2 z^2 (-60 - 314 z + 1053 z^2 - 1119 z^3 + 432 z^4) + y^3 z (-168 - 314 z + 1740 z^2\\&- 2175 z^3 + 972 z^4) + y^4 (18 - 26 z + 1053 z^2 - 2175 z^3 + 1248 z^4)) + 3240 (-1 + y) (-1 + z) (-1 + y + z)\\&\times (y + z)^4 (10 y^3 + 6 y^2 (-2 + z) + y (3 - 6 z + 6 z^2) + z (3 - 12 z + 10 z^2)) H(2, y)^2 - 216 (-1 + y)\\&\times (-1 + z) (y + z)^4 (4 + 16 y^4 - 22 z + 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z + 8 z^2)\\&+ y (-22 + 48 z - 51 z^2 + 20 z^3)) H(3, y) - 6480 (-1 + y) (-1 + z) (-1 + y + z) (y + z)^4 (10 y^3\\&+ 6 y^2 (-2 + z) + y (3 - 6 z + 6 z^2) + z (3 - 12 z + 10 z^2)) H(2, 2, y)) - 216 (-1 + y) (-1 + z) (y + z)^4 \\&\times (4 + 16 y^4 - 22 z + 45 z^2 - 43 z^3 + 16 z^4 + y^3 (-43 + 20 z) + 3 y^2 (15 - 17 z + 8 z^2)\\&+ y (-22 + 48 z - 51 z^2 + 20 z^3)) H(3, 2, y) + 1296 (-1 + y) (-1 + z) z (-1 + y + z) (y + z)^4 (3 - 12 z + 10 z^2\\&+ y (-3 + 6 z)) H(0, 0, 0, y) + 1296 (-1 + y) y (3 + 10 y^2 + 6 y (-2 + z) - 3 z) (-1 + z) (-1 + y + z) (y + z)^4\\&\times H(0, 0, 0, z) - 6480 (-1 + y) (-1 + z) (-1 + y + z) (y + z)^4 (10 y^3 + 6 y^2 (-2 + z) + y (3 - 6 z + 6 z^2)\\&+ z (3 - 12 z + 10 z^2)) H(1, 1, 1, z) - 6480 (-1 + y) (-1 + z) (-1 + y + z) (y + z)^4 (10 y^3 + 6 y^2 (-2 + z) \\&+ y (3 - 6 z + 6 z^2) + z (3 - 12 z + 10 z^2)) H(2, 2, 2, y)\Bigg \}\Big /\Big (864 (-1 + y) y (-1 + z) z (-1 + y + z) (y + z)^4\Big );\\ \mathcal {A}_{3;C_{F}n_{f}}^{(2)}&= \Bigg \{(-1 + y) (-1 + z) ((-1 + z)^2 z^2 (490 - 463 z + 245 z^2) + y^6 (245 - 982 z + 656 z^2)\\&+ y^5 (-953 + 4142 z - 4366 z^2 + 1096 z^3) + y^4 (1661 - 8739 z + 14467 z^2 - 8188 z^3 + 880 z^4) \\&+ y z (980 - 4869 z + 9468 z^2 - 8739 z^3 + 4142 z^4 - 982 z^5) + y^3 (-1443 + 9468 z - 21992 z^2 + 21140 z^3\\&- 8188 z^4 + 1096 z^5) + y^2 (490 - 4869 z + 15614 z^2 - 21992 z^3 + 14467 z^4 - 4366 z^5 + 656 z^6))\\&+ 9 (-1 + y)^2 (-1 + 4 y) (-1 + z)^2 (y + z)^2 (-2 + 2 y^3 + 4 z - 3 z^2 + z^3 + y^2 (-6 + 4 z) + y (6 - 8 z\\&+ 3 z^2)) H(0, y)^2 - 9 (1 - y) (-1 + y) (y^3 + 3 y^2 (-1 + z) + 4 y (-1 + z)^2 + 2 (-1 + z)^3) (-1 + z)^2 (y + z)^2\\&\times (-1 + 4 z) H(0, z)^2 + 63 (1 - y) (-1 + y) (-1 + z)^2 (y + z)^2 (4 + 8 y^4 - 18 z + 33 z^2 - 27 z^3 + 8 z^4\\&+ y^3 (-27 + 20 z) + 3 y^2 (11 - 17 z + 8 z^2) + y (-18 + 48 z - 51 z^2 + 20 z^3)) H(1, z)^2 \\&+ H(0, y) (-27 y (-1 + z)^2 z (-1 + y + z) (y + z)^2 (8 y^3 + y (30 - 27 z) + 12 (-1 + z) + 2 y^2 (-13 + 6 z))\\&- 54 (-1 + y)^2 (-1 + 4 y) (-1 + z)^2 (-1 + y + z) (y + z)^2 (2 + 2 y^2 + 2 y (-2 + z) - 2 z + z^2) H(1, z))\\&+ 27 (1 - y) (-1 + y) (-1 + z)^2 (y^5 (-3 + 20 z) + y^4 (9 - 73 z + 80 z^2) - 3 z^2 (-2 + 4 z - 3 z^2 + z^3)\\&+ 6 y^3 (-2 + 15 z - 34 z^2 + 20 z^3) + y z (-8 - 32 z + 90 z^2 - 73 z^3 + 20 z^4) + 2 y^2 (3 - 16 z + 81 z^2 - 102 z^3\\&+ 40 z^4)) H(2, y) + 63 (1 - y) (-1 + y) (-1 + z)^2 (y + z)^2 (4 + 8 y^4 - 18 z + 33 z^2 - 27 z^3 + 8 z^4 \\&+ y^3 (-27 + 20 z) + 3 y^2 (11 - 17 z + 8 z^2) + y (-18 + 48 z - 51 z^2 + 20 z^3)) H(2, y)^2 + H(0, z)\\&\times (-27 (-1 + y)^2 y z (-1 + y + z) (y + z)^2 (-12 + 30 z - 26 z^2 + 8 z^3 + 3 y (4 - 9 z + 4 z^2))\\&- 54 (-1 + y)^2 (y^2 + 2 y (-1 + z) + 2 (-1 + z)^2) (-1 + z)^2 (-1 + y + z) (y + z)^2 (-1 + 4 z) H(2, y))\\&+ H(1, z) (27 (1 - y) (-1 + y) (-1 + z)^2 (-1 + y + z) (y^4 (-3 + 20 z) - 3 z^2 (2 - 2 z + z^2)\\&+ y^3 (6 - 50 z + 60 z^2) + 2 y z (4 + 17 z - 25 z^2 + 10 z^3) + y^2 (-6 + 34 z - 94 z^2 + 60 z^3))\\&+ 54 (-1 + y)^2 (-1 + z)^2 (-1 + y + z)(y+ z)^2(-4 + 8 y^3 + 14 z - 19 z^2 + 8 z^3 + y^2 (-19 + 12 z) \end{aligned}$$
$$\begin{aligned}&+ 2 y (7 - 10 z + 6 z^2)) H(3, y)) + 18 (1 - y)(1 - 5 y + 4 y^2) (-1 + z)^2 (y + z)\\&\times (2 y^4 + 6 y^3 (-1 + z) + y^2 (6 - 14 z + 7 z^2) + z (-2 + 4 z - 3 z^2 + z^3)+ y (-2 + 10 z - 11 z^2 + 4 z^3))\\&\times H(0, 0, y) + 18 (1 - y) (-1 + y) (-1 + z) (y + z) (1 - 5 z + 4 z^2) (y^4 + 2 (-1 + z)^3 z+ 2 y (-1 + z)^2 \\&\times (-1 + 3 z) + y^3 (-3 + 4 z) + y^2 (4 - 11 z + 7 z^2)) H(0, 0, z) + 54 (-1 + y)^2 (-1 + 4 y) (-1 + z)^2 \\&\times (y + z)^2 (-2 + 2 y^3 + 4 z - 3 z^2 + z^3 + y^2 (-6 + 4 z) + y (6 - 8 z + 3 z^2)) H(0, 1, z) - 54 (-1 + y)^2\\&\times (-1 + 4 y) (-1 + z)^2 (y + z)^2 (-2 + 2 y^3 + 4 z - 3 z^2 + z^3 + y^2 (-6 + 4 z) + y (6 - 8 z + 3 z^2)) H(0, 2, y)\\&+ 54 (-1 + y)^2 (-1 + 4 y) (-1 + z)^2 (y + z)^2 (-2 + 2 y^3 + 4 z - 3 z^2 + z^3 + y^2 (-6 + 4 z) + y (6 - 8 z + 3 z^2))\\&\times H(1, 0, y) + 126 (-1 + y)^2 (-1 + z)^2 (y + z)^2 (4 + 8 y^4 - 18 z + 33 z^2 - 27 z^3 + 8 z^4\\&+ y^3 (-27 + 20 z) + 3 y^2 (11 - 17 z + 8 z^2) + y (-18 + 48 z - 51 z^2 + 20 z^3)) H(1, 1, z) \\&- 54 (-1 + y)^2 (-1 + 4 y) (-1 + z)^2 (y + z)^2 (-2 + 2 y^3 + 4 z - 3 z^2 + z^3 + y^2 (-6 + 4 z)\\&+ y (6 - 8 z + 3 z^2)) H(2, 0, y) + 126 (-1 + y)^2 (-1 + z)^2 (y + z)^2 (4 + 8 y^4 - 18 z + 33 z^2 \\&- 27 z^3 + 8 z^4 + y^3 (-27 + 20 z) + 3 y^2 (11 - 17 z + 8 z^2) + y (-18 + 48 z - 51 z^2 + 20 z^3))\\&\times H(2, 2, y) + 54 (-1 + y)^2 (-1 + z)^2 (y + z)^2 (4 + 8 y^4 - 18 z + 33 z^2 - 27 z^3 + 8 z^4\\&+ y^3 (-27 + 20 z) + 3 y^2 (11 - 17 z + 8 z^2) + y (-18 + 48 z - 51 z^2 + 20 z^3)) H(3, 2, y)\Bigg \}\Big /\\&\times \Big (108 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^2\Big );\\ \mathcal {A}_{4;C_{A}^{2}}^{(2)}&= \frac{39}{20}~ \mathcal {A}_{0}; \qquad \mathcal {A}_{4;C_{F}^{2}}^{(2)} = -\frac{44}{5}~ \mathcal {A}_{0}; \qquad \mathcal {A}_{4;n_{f}^{2}}^{(2)} = 0; \qquad \mathcal {A}_{4;C_{A}C_{F}}^{(2)} = \frac{93}{10}~ \mathcal {A}_{0}; \qquad \mathcal {A}_{4;C_{A}n_{f}}^{(2)} = 0;\qquad \mathcal {A}_{4;C_{F}n_{f}}^{(2)} = 0; \\ \end{aligned}$$
$$\begin{aligned} \mathcal {A}_{5;C_{A}^{2}}^{(2)}&= \Bigg \{6048 y^9 z + (-1 + z)^5 (814 - 814 z + 83 z^2) + 216 y^8 z (-177 + 74 z - 12 z^2 + 3 z^3) + y (-1 + z)^4 \\&\times (4884 - 4916 z - 10029 z^2 + 20360 z^3 - 14040 z^4 + 6048 z^5) + y^7 (83 + 112808 z - 124552 z^2 + 79000 z^3\\&- 39863 z^4 + 8812 z^5)+ y^2 (-1 + z)^3 (12293 - 2060 z - 65043 z^2 + 119980 z^3 - 76600 z^4 + 15984 z^5) \\&- y^3 (-1 + z)^2 (-16695 - 44834 z + 223663 z^2 - 364320 z^3 + 263636 z^4 - 73816 z^5 + 2592 z^6)\\&+ y^6 (-1229 - 199901 z + 397732 z^2 - 413860 z^3 + 281873 z^4 - 103639 z^5 + 14832 z^6) + y^5 (5714\\&+ 219568 z - 670767 z^2 + 965408 z^3 - 836204 z^4 + 417156 z^5 - 103639 z^6 + 8812 z^7)\\&+ y^4 (-13040 - 131106 z + 629609 z^2 - 1215939 z^3 + 1324022 z^4 - 836204 z^5 + 281873 z^6 - 39863 z^7\\&+ 648 z^8) + 36 (-1 + y)^4 (-1 + z)^4 (2 + y^2 (3 - 9 z) - 4 z + 3 z^2 - z^3 + y^3 (-1 + 4 z) \\&+ y (-4 + 12 z - 9 z^2 + 4 z^3)) H(0, y) + 36 (-1 + y)^4 (-1 + z)^4 (2 + y^2 (3 - 9 z) - 4 z + 3 z^2\\&- z^3 + y^3 (-1 + 4 z) + y (-4 + 12 z - 9 z^2 + 4 z^3)) H(0, z) - 36 (-1 + y)^4 (-1 + z)^4 \\&\times (220 y^4 + y^3 (-443 + 324 z) + 3 y^2 (81 - 117 z + 32 z^2) + y (-8 + 24 z + 6 z^2 - 24 z^3)\\&+ 6 (-2 + 4 z - 3 z^2 + z^3)) H(1, y) + 36 (-1 + y)^4 (-1 + z)^4 (220 y^4 + 4 y^3 (-111 + 82 z)\\&+ 6 y^2 (41 - 60 z + 16 z^2) + 5 (-2 + 4 z - 3 z^2 + z^3) - y (12 - 36 z + 3 z^2 + 20 z^3)) H(1, z)\\&+ 72 (-1 + y)^4 (-1 + z)^4 (-11 + 110 y^4 + 6 z + 114 z^2 - 219 z^3 + 110 z^4 + y^3 (-219 + 152 z)\\&+ 3 y^2 (38 - 59 z + 32 z^2) + y (6 + 30 z - 177 z^2 + 152 z^3)) H(2, y)\Bigg \}\Big / \Big (144 (-1 + y)^4 y (-1 + z)^4 z (-1 + y + z)\Big );\\ \mathcal {A}_{5;C_{F}^{2}}^{(2)}&= \Bigg \{-432 y^9 z - 6 (-1 + z)^5 (31 - 30 z + 20 z^2) - 12 y^8 z (-261 + 147 z - 40 z^2 + 10 z^3)\\&- 6 y (-1 + z)^4 (185 - 354 z + 224 z^2 + 102 z^3 - 234 z^4 + 72 z^5) + y^7 (-120 - 8820 z + 8139 z^2 - 1414 z^3 \\&- 733 z^4 + 356 z^5) - 3 y^2 (-1 + z)^3 (960 - 2620 z + 2922 z^2 - 754 z^3 - 949 z^4 + 588 z^5) + y^3 (-1 + z)^2\\&\times (-4260 + 13428 z - 23904 z^2 + 19624 z^3 - 6031 z^4 - 454 z^5 + 480 z^6)\\&+ y^6 (780 + 11256 z - 11571 z^2 - 4643 z^3 + 9499 z^4 - 4121 z^5 + 528 z^6)\\&+ y^5 (-2286 - 2220 z - 5247 z^2 + 31232 z^3 - 36206 z^4 + 18060 z^5 - 4121 z^6 + 356 z^7) \\&+ y^4 (3930 - 13818 z + 38097 z^2 - 69183 z^3 + 68534 z^4 - 36206 z^5 + 9499 z^6 - 733 z^7\\&- 120 z^8) - 12 (-1 + y)^4 (-1 + z)^4 (14 y^4 + 6 y^2 (-3 + z) z + y^3 (-23 + 28 z)\\&+ y (13 - 18 z + 15 z^2 - 8 z^3) + 2 (-2 + 4 z - 3 z^2 + z^3)) H(1, y) + 12 (-1 + y)^4 (-1 + z)^4\\&\times (2 + 14 y^4 - 4 z + 3 z^2 - z^3 + y^3 (-26 + 40 z) + y^2 (9 - 45 z + 6 z^2) + y (1 + 18 z - 12 z^2 + 4 z^3))\\&\times H(1, z) + 12 (-1 + y)^4 (-1 + z)^4 (-2 + 14 y^4 + 9 z + 3 z^2 - 24 z^3 + 14 z^4 + 8 y^3 (-3 + 4 z) \\&+ 3 y^2 (1 - 10 z + 4 z^2) + y (9 - 30 z^2 + 32 z^3)) H(2, y)\Bigg \}\Big / \Big (6 (-1 + y)^4 y (-1 + z)^4 z (-1 + y + z)\Big );\\ \mathcal {A}_{5;n_{f}^{2}}^{(2)}&= 0;\\ \end{aligned}$$
$$\begin{aligned} \mathcal {A}_{5;C_{A}C_{F}}^{(2)}&= \Bigg \{3456 y^9 z + (-1 + z)^5 (2470 - 2290 z + 1613 z^2) + 72 y^8 z (-351 + 207 z - 64 z^2 + 16 z^3)\\&+ y^7 (1613 + 64136 z - 47008 z^2 - 12968 z^3 + 21871 z^4 - 6908 z^5) + y (-1 + z)^4 (14640 - 32276 z \\&+ 25053 z^2 - 2392 z^3 - 11448 z^4 + 3456 z^5) + y^2 (-1 + z)^3 (37763 - 128708 z + 163755 z^2 - 83348 z^3 \\&- 2296 z^4 + 14904 z^5) - y^3 (-1 + z)^2 (-55665 + 243490 z - 455855 z^2 + 399648 z^3 - 166612 z^4 + 22184 z^5\\&+ 4608 z^6) - y^6 (10355 + 47891 z + 31748 z^2 - 206372 z^3 + 191809 z^4 - 69095 z^5 + 7488 z^6)\\&+ y^5 (30050 - 97592 z + 392007 z^2 - 755056 z^3 + 679888 z^4 - 308028 z^5 + 69095 z^6 - 6908 z^7)\\&+ y^4 (-51380 + 292182 z - 867721 z^2 + 1421763 z^3 - 1305946 z^4 + 679888 z^5 - 191809 z^6 + 21871 z^7 \\&+ 1152 z^8) + 36 (-1 + y)^4 (-1 + z)^4 (64 y^4 + 18 y^2 z (-5 + 2 z) + 4 y^3 (-27 + 34 z)\\&+ y (66 - 96 z + 81 z^2 - 44 z^3) + 11 (-2 + 4 z - 3 z^2 + z^3)) H(1, y) - 36 (-1 + y)^4 (-1 + z)^4\\&\times (4 + 64 y^4 - 8 z + 6 z^2 - 2 z^3 + y^3 (-121 + 188 z) + 3 y^2 (13 - 69 z + 12 z^2) + 2 y (7 + 30 z\\&- 18 z^2 + 4 z^3)) H(1, z) - 72 (-1 + y)^4 (-1 + z)^4 (-9 + 32 y^4 + 29 z + 3 z^2 - 55 z^3 + 32 z^4\\&+ y^3 (-55 + 72 z) + y^2 (3 - 63 z + 36 z^2) + y (29 - 18 z - 63 z^2 + 72 z^3)) H(2, y)\Bigg \}\Big /\\&\times \Big (72 (-1 + y)^4 y (-1 + z)^4 z (-1 + y + z)\Big );\\ \mathcal {A}_{5;C_{A}n_{f}}^{(2)}&= \Bigg \{-1296 y^9 z - 37 (-1 + z)^5 (2 - 2 z + z^2) - 18 y^8 z (-459 + 177 z - 8 z^2 + 2 z^3) - y^7 (37 + 23464 z\\&\ \ - 21866 z^2 + 9620 z^3 - 4555 z^4 + 1076 z^5) - y (-1 + z)^4 (444 - 388 z - 1653 z^2 + 3376 z^3 - 3078 z^4\\&\ \ + 1296 z^5) - y^2 (-1 + z)^3 (1147 + 878 z - 10719 z^2 + 18518 z^3 - 12308 z^4 + 3186 z^5)\\&\ \ + y^6 (259 + 38809 z - 65000 z^2 + 56576 z^3 - 38287 z^4 + 15203 z^5 - 2376 z^6)\\&\ \ + y^3 (-1 + z)^2 (-1665 - 9214 z + 35399 z^2 - 55404 z^3 + 37768 z^4 - 9332 z^5 + 144 z^6) \\&\ y^5 (814 + 40088 z - 106383 z^2 + 140272 z^3 - 121660 z^4 + 62292 z^5 - 15203 z^6 + 1076 z^7)\\&\ \ + y^4 (1480 + 24504 z - 100897 z^2 + 183975 z^3 - 196954 z^4 + 121660 z^5 - 38287 z^6 + 4555 z^7 - 36 z^8) \\&\ \ + 108 (-1 + y)^4 y (-1 + z)^4 (10 y^3 - 3 (-1 + z)^2 + 2 y^2 (-11 + 8 z) + 3 y (5 - 7 z\\&+ 2 z^2)) H(1, y) - 108 (-1 + y)^4 y (-1 + z)^4 (10 y^3 - 3 (-1 + z)^2 + 2 y^2 (-11 + 8 z) + 3 y (5 - 7 z + 2 z^2)) \\&\ \ \times H(1, z) - 108 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (10 y^3 + 6 y^2 (-2 + z) + y (3 - 6 z + 6 z^2) \\&\ \ + z (3 - 12 z + 10 z^2)) H(2, y)\Bigg \}\Big /\Big (72 (-1 + y)^4 y (-1 + z)^4 z (-1 + y + z)\Big );\\ \mathcal {A}_{5;C_{F}n_{f}}^{(2)}&= -\frac{1}{9} ~ \mathcal {A}_{0}; \end{aligned}$$
$$\begin{aligned} \mathcal {A}_{6;C_{A}^{2}}^{(2)}&= \Bigg \{8 (-1 + y) (-1 + z) (y + z) (-1008 y^{12} z + 4 (-1 + z)^4 z^5 (10 - z + 5 z^2) \\&\ \ + 4 y^{11} (5 + 622 z - 51 z^2 - 1631 z^3 + 551 z^4) - y (-1 + z)^3 z^4 (200 - 96 z + 1182 z^2 - 2503 z^3 + 536 z^4 \\&\ \ + 1008 z^5) + y^{10} (-84 + 1087 z - 12868 z^2 + 50961 z^3 - 50902 z^4 + 13822 z^5) - y^2 (-1 + z)^2 \\&\ \ \times z^3 (-400 + 3298 z - 10431 z^2 + 24380 z^3 - 31260 z^4 + 13276 z^5 + 204 z^6) + y^9 (176 - 9291 z \\&\ \ + 57608 z^2 - 186114 z^3 + 279822 z^4 - 174455 z^5 + 38302 z^6) + y^8 (-264 + 11687 z - 100176 z^2 + 374314 z^3 \\&\ \ - 739622 z^4+ 736539 z^5 - 343702 z^6 + 61224 z^7) + y^7 (276 - 6537 z + 90451 z^2 - 436329 z^3 + 1100987 z^4 \\&\ \ - 1543684 z^5 + 1154814 z^6 - 427250 z^7 + 61224 z^8) + y^3 z^2 (400 - 4252 z + 32055 z^2 - 129393 z^3 \\&\ \ + 304882 z^4 - 436329 z^5 + 374314 z^6 - 186114 z^7 + 50961 z^8 - 6524 z^9) + 2 y^6 (-82 + 1035 z - 24270 z^2 \\&\ \ + 152441 z^3 - 484929 z^4 + 903470 z^5 - 973380 z^6 + 577407 z^7 - 171851 z^8 + 19151 z^9) \\&\ \ + y^4 z (200 - 4098 z + 32055 z^2 - 165612 z^3 + 515832 z^4 - 969858 z^5 + 1100987 z^6 - 739622 z^7\\&\ \ + 279822 z^8 - 50902 z^9 + 2204 z^{10}) + y^5 (40 - 696 z + 17427 z^2 - 129393 z^3 + 515832 z^4 - 1240356 z^5 \\&\ \ + 1806940 z^6 - 1543684 z^7 + 736539 z^8 - 174455 z^9 + 13822 z^{10})) - 9 (-1 + y)^4 (-1 + z)^4 (y + z)^6 \\&\ \ \times (496 y^4 + y^3 (-1129 + 1244 z) + 3 y^2 (213 - 557 z + 284 z^2) + y (62 + 444 z - 870 z^2 + 416 z^3) \\&\ \ + 4 (-17 - 46 z + 234 z^2 - 301 z^3 + 130 z^4)) H(0, y)^2 - 9 (-1 + y)^4 (-1 + z)^4 (y + z)^6 \\&\ \ \times (-68 + 520 y^4 + 62 z + 639 z^2 - 1129 z^3 + 496 z^4 + 4 y^3 (-301 + 104 z) + y^2 (936 - 870 z + 852 z^2) \\&\ \ + y (-184 + 444 z - 1671 z^2 + 1244 z^3)) H(0, z)^2 + 9 (-1 + y)^4 (-1 + z)^4 (y + z)^6 (-104 + 992 y^4 + 246 z \\&\ \ + 861 z^2 - 1995 z^3 + 992 z^4 + 5 y^3 (-399 + 436 z) + 3 y^2 (287 - 881 z + 440 z^2) \\&\ \ + y (246 + 696 z - 2643 z^2 + 2180 z^3)) H(1, z)^2 + H(1, y) (-48 (-1 + y)^3 (-1 + z)^4 (y + z)^6 \\&\ \ \times (-98 + 160 y^5 + 247 z - 279 z^2 + 96 z^3 + y^4 (-697 + 232 z) + y^3 (1221 - 871 z + 318 z^2) \\&\ \ + y (503 - 856 z + 768 z^2 - 192 z^3) + 3 y^2 (-363 + 416 z - 270 z^2 + 32 z^3)) + 144 (-1 + y)^4 (-1 + z)^4 \\&\ \ \times (y + z)^6 (84 y^4 + y^3 (-193 + 76 z) + 3 y^2 (51 - 39 z + 16 z^2) + 2 (-2 + 4 z - 3 z^2 + z^3) \\&\ \ - 2 y (20 - 12 z + 3 z^2 + 4 z^3)) H(1, z)) - 12 (672 y^{15} z - (-1 + z)^5 z^6 (-306 + 1094 z - 1417 z^2 + 640 z^3) \\&\ \ - 8 y^{14} (80 + 211 z - 246 z^2 - 284 z^3 + 71 z^4) - 3 y^{13} (-1539 + 3624 z - 2740 z^2 + 6256 z^3 - 6117 z^4 \\&\ \ + 1188 z^5) + y^{12} (-14579 + 71063 z - 127704 z^2 + 152312 z^3 - 144029 z^4 + 67593 z^5 - 10032 z^6) \end{aligned}$$
$$\begin{aligned}&+ y (-1 + z)^4 z^5 (-1644 + 10824 z - 23462 z^2 + 24135 z^3 - 10904 z^4 + 1000 z^5 + 672 z^6)\\&\ \ + 6 y^2 (-1 + z)^3 z^4 (947 - 7217 z + 22516 z^2 - 36737 z^3 + 33102 z^4 - 15206 z^5 + 2354 z^6 + 328 z^7) \\&\ \ - 2 y^{11} (-13173 + 94377 z - 256362 z^2 + 378172 z^3 - 374314 z^4 + 238281 z^5 - 76309 z^6 + 8656 z^7) \\&\ \ - 2 y^{10} (14920 - 147049 z + 552045 z^2 - 1083308 z^3 + 1307983 z^4 - 1034540 z^5 + 496204 z^6 \\&\ \ - 121179 z^7 + 10892 z^8) + y^9 (21725 - 293156 z + 1483434 z^2 - 3858986 z^3 + 5967465 z^4\\&\ \ - 5942620 z^5 + 3826296 z^6 - 1476766 z^7 + 296968 z^8 - 23016 z^9) + 2 y^3 (-1 + z)^2 z^3 (-3384 + 44062 z \\&\ \ - 198605 z^2 + 462415 z^3 - 632873 z^4 + 523576 z^5 - 249468 z^6 + 60796 z^7 - 7112 z^8 + 1136 z^9) \\&\ \ + y^8 (-9947 + 189503 z - 1308468 z^2 + 4503474 z^3 - 8996757 z^4 + 11383863 z^5 - 9480686 z^6 + 5112368 z^7 \\&\ \ - 1673910 z^8 + 296968 z^9 - 21784 z^{10}) - 2 y^7 (-1312 + 38311 z - 380649 z^2 + 1756308 z^3 - 4551510 z^4 \\&\ \ + 7339866 z^5 - 7783882 z^6 + 5514200 z^7 - 2556184 z^8 + 738383 z^9 - 121179 z^{10} + 8656 z^{11}) \\&\ \ + y^5 z (-1644 + 60348 z - 580226 z^2 + 2711300 z^3 - 7384344 z^4 + 12777180 z^5 - 14679732 z^6 + 11383863 z^7\\&\ \ - 5942620 z^8 + 2069080 z^9 - 476562 z^{10} + 67593 z^{11} - 3564 z^{12}) + y^4 z^2 (-5682 + 101660 z - 722026 z^2 \\&\ \ + 2711300 z^3 - 6165396 z^4 + 9103020 z^5 - 8996757 z^6 + 5967465 z^7 - 2615966 z^8 + 748628 z^9 - 144029 z^{10} \\&\ \ + 18351 z^{11} - 568 z^{12}) - 2 y^6 (153 - 8700 z + 141024 z^2 - 903687 z^3 + 3082698 z^4 - 6388590 z^5 \\&\ \ + 8608206 z^6 - 7783882 z^7 + 4740343 z^8 - 1913148 z^9 + 496204 z^{10} - 76309 z^{11} + 5016 z^{12})) H(2, y) \\&\ \ + 9 (-1 + y)^4 (-1 + z)^4 (y + z)^6 (-104 + 992 y^4 + 246 z + 861 z^2 - 1995 z^3 + 992 z^4 + 5 y^3 (-399 + 436 z) \\&\ \ + 3 y^2 (287 - 881 z + 440 z^2) + y (246 + 696 z - 2643 z^2 + 2180 z^3)) H(2, y)^2 + H(0, y) (-12 (-1 + y)^3 \\&\ \ \times (y + z)^6 (672 y^6 z + 49 (-1 + z)^5 (2 - 2 z + z^2) + 24 y^5 z (-93 + 74 z - 12 z^2 + 3 z^3) - y (-1 + z)^4 \\&\ \ \times (-306 + 1096 z - 1680 z^2 + 1205 z^3) + y^3 (-1 + z)^2 (304 - 3453 z + 4062 z^2 - 2983 z^3 + 984 z^4) \end{aligned}$$
$$\begin{aligned}&\ \ + y^2 (-1 + z)^3 (415 - 2620 z + 4200 z^2- 3661 z^3 + 1156 z^4) + y^4 (-97 + 3488 z - 6112 z^2\\&\ + 3784 z^3 - 1283 z^4 + 220 z^5)) - 432 (-1 + y)^4 (-1 + z)^4 (y + z)^6 (2 + y^2 (3 - 9 z)\\&\ - 4 z + 3 z^2 - z^3 + y^3 (-1 + 4 z) + y (-4 + 12 z - 9 z^2 + 4 z^3)) H(0, z) \\&\ + 144 (-1 + y)^4 (-1 + z)^4 (y + z)^6 (22 y^3 + 4 y^4 - 6 y^2 (10 - 9 z + 4 z^2) + y (40 - 60 z + 39 z^2 - 12 z^3)\\&\ + 3 (-2 + 4 z - 3 z^2 + z^3)) H(1, z) + 144 (-1 + y)^4 (-1 + z)^4 (y + z)^6 (2 + y^2 (3 - 9 z) - 4 z + 3 z^2 - z^3 \\&\ + y^3 (-1 + 4 z) + y (-4 + 12 z - 9 z^2 + 4 z^3)) H(2, y)) + H(0, z) (-12 (-1 + z)^3 (y + z)^6 (-((-1 + z)^2\\&\ \times (98 - 110 z + 97 z^2)) + y^7 (49 - 1205 z + 1156 z^2) + y^6 (-343 + 6500 z - 7129 z^2 + 984 z^3)\\&\ + y^5 (1078 - 15046 z + 18651 z^2 - 4951 z^3 + 220 z^4) + y^3 (2205 - 15725 z + 24536 z^2 - 14560 z^3 \\&\ + 3784 z^4 - 288 z^5) + y^4 (-1960 + 19590 z - 27359 z^2 + 11012 z^3 - 1283 z^4 + 72 z^5)\\&\ + y^2 (-1519 + 7900 z - 13305 z^2 + 11272 z^3 - 6112 z^4 + 1776 z^5) + y (588 - 2320 z + 3865 z^2\\&\ - 4061 z^3 + 3488 z^4 - 2232 z^5 + 672 z^6)) + 144 (-1 + y)^4 (-1 + z)^4 (y + z)^6 (88 y^4 \\&\ + y^3 (-201 + 124 z) + 3 y^2 (49 - 57 z + 20 z^2) + 2 (-2 + 4 z - 3 z^2 + z^3) - 2 y (15 - 18 z + 6 z^2\\&\ + 4 z^3)) H(1, y) + 144 (-1 + y)^4 (-1 + z)^4 (y + z)^6 (2 + y^2 (3 - 9 z) - 4 z + 3 z^2 - z^3 + y^3 (-1 + 4 z)\\&\ + y (-4 + 12 z - 9 z^2 + 4 z^3)) H(1, z) - 288 (-1 + y)^4 (-1 + z)^4 (y + z)^6 (44 y^4 + 34 y^3 (-3 + 2 z)\\&\ - (-1 + z)^2 (-1 + 14 z + 2 z^2) + 3 y^2 (26 - 35 z + 14 z^2) - y (21 - 48 z + 33 z^2 + 4 z^3)) H(2, y)) \\&\ + H(1, z) (-12 (672 y^{15} z - (-1 + z)^5 z^6 (86 - 134 z + 91 z^2) - 8 y^{14} (80 + 211 z - 246 z^2\\&\ - 284 z^3 + 71 z^4) - 3 y^{13} (-1411 + 2984 z - 1460 z^2 + 4976 z^3 - 5477 z^4 + 1060 z^5)\\&\ + y^{12} (-11927 + 54659 z - 85020 z^2 + 92588 z^3 - 96701 z^4 + 47481 z^5 - 6456 z^6) + y (-1 + z)^4 z^5\\&\ \times (708 - 1452 z + 1870 z^2 - 2253 z^3 + 2456 z^4 - 1560 z^5 + 672 z^6)\\&\ - 2 y^{11} (-9295 + 64627 z - 158940 z^2 + 201252 z^3 - 181596 z^4 + 112239 z^5 - 30455 z^6 \end{aligned}$$
$$\begin{aligned}&+ 1496 z^7) + 2 y^2 (-1 + z)^3 z^4 (-99 + 1107 z - 3248 z^2 + 8087 z^3 - 15336 z^4 + 17678 z^5 - 10838 z^6 + 2904 z^7)\\&+ 2 y^{10} (-8632 + 86311 z - 304059 z^2 + 516984 z^3 - 511401 z^4 + 325416 z^5 - 105440 z^6 - 739 z^7 \\&+ 5592 z^8) - 2 y^3 (-1 + z)^2 z^3 (-536 - 852 z + 7455 z^2 - 903 z^3 - 46165 z^4 + 106706 z^5 - 114712 z^6\\&+ 62368 z^7 - 14048 z^8 + 144 z^9) + 3 y^9 (3127 - 46340 z + 231586 z^2 - 539722 z^3 + 671983 z^4 - 471956 z^5\\&+ 148964 z^6 + 36522 z^7 - 42364 z^8 + 8648 z^9) + y^8 (-2527 + 64339 z - 489624 z^2 + 1601594 z^3 - 2644553 z^4\\&+ 2271207 z^5 - 738570 z^6 - 439680 z^7 + 556890 z^8 - 212212 z^9 + 27760 z^{10})\\&+ 2 y^7 (34 - 6481 z + 102519 z^2 - 502456 z^3 + 1134338 z^4 - 1263358 z^5 + 486190 z^6 + 442468 z^7 - 684158 z^8 \\&+ 375311 z^9 - 94127 z^{10} + 8712 z^{11}) + y^4 z^2 (198 + 2720 z - 54406 z^2 + 215036 z^3 - 276280 z^4 \\&- 222736 z^5 + 1183523 z^6 - 1711791 z^7 + 1308226 z^8 - 546976 z^9 + 107843 z^{10} - 5429 z^{11} + 72 z^{12})\\&+ y^5 z (708 + 2880 z - 75318 z^2 + 390360 z^3 - 862488 z^4 + 683692 z^5 + 668588 z^6 - 2089833 z^7\\&+ 2146884 z^8 - 1135548 z^9 + 302226 z^{10} - 32683 z^{11} + 1204 z^{12}) + 2 y^6 (43 - 562 z - 22170 z^2\\&+ 191307 z^3 - 617668 z^4 + 934096 z^5 - 486604 z^6 - 520444 z^7 + 1071647 z^8 - 795420 z^9 + 294048 z^{10}\\&- 50805 z^{11} + 3204 z^{12})) - 144 (-1 + y)^4 (-1 + z)^4 (y + z)^6 (100 y^4 + 2 y^3 (-127 + 60 z)\\&+ 6 y^2 (38 - 41 z + 24 z^2) + z (-38 + 153 z - 203 z^2 + 88 z^3) + y (-74 + 144 z - 231 z^2 + 132 z^3)) H(2, y)\\&- 144 (-1 + y)^4 (-1 + z)^4 (y + z)^6 (-4 + 36 y^4 - 4 z + 51 z^2 - 79 z^3 + 36 z^4 + y^3 (-79 + 52 z)\\&+ y^2 (51 - 75 z + 48 z^2) + y (-4 + 24 z - 75 z^2 + 52 z^3)) H(3, y)) + 18 (-1 + y)^4 (-1 + z)^4 (y + z)^6\\&\times (496 y^4 + y^3 (-1129 + 1244 z) + 3 y^2 (213 - 557 z + 284 z^2) + y (62 + 444 z - 870 z^2 + 416 z^3)\\&+ 4 (-17 - 46 z + 234 z^2 - 301 z^3 + 130 z^4)) H(0, 0, y) + 18 (-1 + y)^4 (-1 + z)^4 (y + z)^6\\&\times (-68 + 520 y^4 + 62 z + 639 z^2 - 1129 z^3 + 496 z^4 + 4 y^3 (-301 + 104 z) + y^2 (936 - 870 z + 852 z^2)\\&+ y (-184 + 444 z - 1671 z^2 + 1244 z^3)) H(0, 0, z) - 288 (-1 + y)^4 (-1 + z)^4 (y + z)^6 (2 + 10 y^4 - 4 z + 3 z^2\\&\times - z^3 + 7 y^3 (-3 + 4 z) + 6 y^2 (2 - 6 z + z^2) + y (-3 + 18 z - 12 z^2 + 4 z^3))\\&\times H(0, 1, z) + 144 (-1 + y)^4 (-1 + z)^4 (y + z)^6 (-8 + 36 y^4 + 2 z + 27 z^2 - 37 z^3 + 16 z^4 + 11 y^3 (-7 + 4 z)\\&+ y^2 (45 - 51 z + 36 z^2) - y (-4 + 12 z + 3 z^2 + 4 z^3)) H(0, 2, y) - 144 (-1 + y)^4 y (-1 + z)^4 (y + z)^6\\&\times (4 y^3 + y^2 (19 + 12 z) + 4 (7 - 6 z + 3 z^2) - 3 y (17 - 9 z + 8 z^2)) H(1, 0, y) - 144 (-1 + y)^4 (-1 + z)^4\\&\times (-1 + y + z) (y + z)^6 (88 y^3 + 13 y^2 (-9 + 4 z) - 2 (2 - 2 z + z^2) + y (42 - 38 z + 8 z^2)) \\&\times H(1, 0, z) + 288 (-1 + y)^4 y (-1 + z)^4 (y + z)^6 (5 + 2 y^3 + 6 z - 3 z^2 + 4 y^2 (-1 + 6 z) + 3 y (-1 - 9 z + 2 z^2)) \\&\times H(1, 1, y)- 18 (-1 + y)^4 (-1 + z)^4 (y + z)^6 (-72 + 1792 y^4 + 182 z + 909 z^2 - 2011 z^3 + 992 z^4\\&+ y^3 (-4043 + 3204 z) + 3 y^2 (911 - 1505 z + 664 z^2) + y (-410 + 1560 z - 3123 z^2 + 2244 z^3)) H(1, 1, z)\\&+ 144 (-1 + y)^4 (-1 + z)^4 (y + z)^6 (84 y^4 + y^3 (-193 + 76 z) + 3 y^2 (51 - 39 z + 16 z^2)\\&+ 2 (-2 + 4 z - 3 z^2 + z^3) - 2 y (20 - 12 z + 3 z^2 + 4 z^3)) H(1, 2, y) + 144 (-1 + y)^4 (-1 + z)^4\\&\times (y + z)^6 (-4 + 4 y^4 + 46 z - 159 z^2 + 205 z^3 - 88 z^4 + y^3 (21 + 4 z) + y^2 (-57 + 75 z - 84 z^2)\\&+ y (36 - 108 z + 219 z^2 - 140 z^3)) H(2, 0, y) - 144 (-1 + y)^4 (-1 + z)^4 (y + z)^6 (20 y^4 + y^3 (-49 + 60 z)\\&+ 3 y^2 (11 - 35 z + 24 z^2) + 4 z (-10 + 27 z - 25 z^2 + 8 z^3) + 4 y (-1 + 18 z - 30 z^2 + 12 z^3)) H(2, 1, y)\\&- 18 (-1 + y)^4 (-1 + z)^4 (y + z)^6 (-104 + 1536 y^4 - 26 z + 1821 z^2 - 3227 z^3 + 1536 z^4 + y^3 (-3227 + 2756 z)\\&+ 3 y^2 (607 - 1217 z + 632 z^2) + y (-26 + 1272 z - 3651 z^2 + 2756 z^3)) H(2, 2, y) - 144 (-1 + y)^4 (-1 + z)^4 \\&\times (y + z)^6 (-4 + 36 y^4 - 4 z + 51 z^2 - 79 z^3 + 36 z^4 + y^3 (-79 + 52 z) + y^2 (51 - 75 z + 48 z^2)\\&+ y (-4 + 24 z - 75 z^2 + 52 z^3)) H(3, 2, y)\Bigg \}\Big / \Big (576 (-1 + y)^4 y (-1 + z)^4 z (-1 + y + z) (y + z)^6\Big );\\ \mathcal {A}_{6;C_{F}^{2}}^{(2)}&= \Bigg \{4 (-1 + y) (-1 + z) (y + z) (288 y^{13} z - 3 (-1 + z)^5 z^5 (90 - 90 z + 43 z^2) + y^{12} (-129 - 1327 z\\&+ 1720 z^2 + 488 z^3 - 176 z^4) + y^{11} (915 + 342 z - 6679 z^2 + 3734 z^3 + 1168 z^4 - 56 z^5)\\&\qquad + y (-1 + z)^4 z^4 (1350 - 4968 z + 5525 z^2 - 2086 z^3 - 175 z^4 + 288 z^5) + y^2 (-1 + z)^3 \\&\times z^3 (-2700 + 15672 z - 38367 z^2 + 41471 z^3 - 16563 z^4 - 1519 z^5 + 1720 z^6) + y^{10} (-2910+ 11667 z \end{aligned}$$
$$\begin{aligned}&- 6846 z^2 - 9291 z^3 + 9388 z^4 - 7000 z^5 + 3264 z^6) + y^9 (5340 - 38596 z + 84883 z^2 - 66628 z^3 \\&+ 1089 z^4 + 39320 z^5 - 36152 z^6 + 10744 z^7) + y^3 (-1 + z)^2 z^2 (2700 - 29448 z + 105101 z^2 - 188876 z^3 \\&+ 176750 z^4 - 72056 z^5 - 359 z^6 + 4710 z^7 + 488 z^8) + y^8 (-6045 + 62541 z - 210950 z^2 + 320503 z^3\\&- 225267 z^4 + 21438 z^5 + 93980 z^6 - 69672 z^7 + 15200 z^8) + y^7 (4179 - 59394 z + 271749 z^2 - 614432 z^3\\&+ 753510 z^4 - 469026 z^5 + 49426 z^6 + 123492 z^7 - 69672 z^8 + 10744 z^9) + y^6 (-1620 + 33497 z - 206288 z^2\\&+ 659603 z^3 - 1187244 z^4 + 1201898 z^5 - 610940 z^6 + 49426 z^7 + 93980 z^8 - 36152 z^9 + 3264 z^{10}) + y^4 z (1350\\&- 23772 z + 166697 z^2 - 565574 z^3 + 1068831 z^4 - 1187244 z^5 + 753510 z^6 - 225267 z^7 + 1089 z^8 + 9388 z^9\\&+ 1168 z^{10} - 176 z^{11}) + y^5 (270 - 10368 z + 93483 z^2 - 428526 z^3 + 1068831 z^4 - 1510552 z^5 \\&+ 1201898 z^6 - 469026 z^7 + 21438 z^8 + 39320 z^9 - 7000 z^{10} - 56 z^{11})) - 3 (-1 + y)^4 (-1 + z)^4\\&\times (-1 + y + z)^2 (y + z)^6 (46 + 704 y^3 - 112 z + 254 z^2 - 192 z^3 + y^2 (-717 + 404 z)\\&- 2 y (-21 + 11 z + 88 z^2)) H(0, y)^2 + 3 (-1 + y)^4 (-1 + z)^4 (-1 + y + z)^2 (y + z)^6 (-46 + 192 y^3 - 42 z\\&+ 717 z^2 - 704 z^3 + 2 y^2 (-127 + 88 z) + y (112 + 22 z - 404 z^2)) H(0, z)^2 + 9 (-1 + y)^4 (-1 + z)^4 (-1 + y + z)^2\\&\times (y + z)^6 (4 + 56 y^3 + 34 z - 101 z^2 + 56 z^3 + y^2 (-101 + 84 z) + y (34 - 76 z + 84 z^2)) H(1, z)^2\\&+ H(1, y) (-8 (-1 + y)^2 (-1 + z)^4 (-1 + y + z) (y + z)^6 (150 + 136 y^6 - 406 z + 411 z^2 - 155 z^3 + y^5 (-761 \\&+ 460 z)+ y^4 (1819 - 2033 z + 456 z^2) + y^2 (1859 - 3607 z + 2367 z^2 - 465 z^3) + y^3 (-2401 + 3730 z \\&- 1665 z^2 + 164 z^3)+ y (-802 + 1856 z - 1569 z^2 + 474 z^3)) - 96 (-1 + y)^4 y (-1 + z)^4 \end{aligned}$$
$$\begin{aligned}&\times (-1 + y + z)^2 (y + z)^6 (3 + 14 y^2 - 3 z+ 3 y (-5 + 2 z)) H(1, z)) + H(0, y) (8 (-1 + y)^2 y (-1 + y + z)^2 \\&\times (y+ z)^6 (144 y^5 z + 12 (-1 + z)^3 z (7 - 6 z + z^2) + 4 y^4 z (-153 + 111 z - 40 z^2 + 10 z^3) - 3 y (-1 + z)^2\\&\times (-4 - 162 z + 220 z^2 - 108 z^3 + 11 z^4) + y^3 (12 + 1112 z - 1955 z^2 + 1610 z^3 - 799 z^4 + 164 z^5) \\&+ 2 y^2 (-12 - 511 z + 1395 z^2 - 1516 z^3 + 831 z^4 - 189 z^5 + 2 z^6)) + 144 (-1 + y)^4 y (-1 + z)^4\\&\times (-1 + y + z)^2 (y + z)^6 (4 + 12 y^2 - 4 z + y (-15 + 8 z)) H(1, z)) + 8 (-1 + y + z) (144 y^{15} z\\&+ (-1 + z)^5 z^6 (-132 + 340 z - 341 z^2 + 136 z^3) + 4 y^{14} (34 - 397 z + 567 z^2 - 176 z^3 + 44 z^4)\\&+ y^{13} (-1021 + 8884 z - 22137 z^2 + 20586 z^3 - 8560 z^4 + 1816 z^5) + y (-1 + z)^4 z^5 (468 - 3576 z + 7726 z^2 \\&- 7779 z^3 + 3972 z^4 - 1012 z^5 + 144 z^6) + y^{12} (3405 - 30315 z + 100809 z^2 - 152893 z^3 + 116054 z^4\\&- 46660 z^5 + 8448 z^6) + 3 y^2 (-1 + z)^3 z^4 (-748 + 5012 z - 15992 z^2 + 27958 z^3 - 27830 z^4 + 16002 z^5\\&- 5111 z^6 + 756 z^7) + y^{11} (-6602 + 66866 z - 275775 z^2 + 575010 z^3 - 652809 z^4 + 420138 z^5- 149708 z^6\\&+ 23168 z^7) + y^{10} (8150 - 98054 z + 493695 z^2 - 1321709 z^3 + 2031803 z^4 - 1859997 z^5 + 1019924 z^6\\&- 313380 z^7 + 41296 z^8) - y^3 (-1 + z)^2 z^3 (-1416 + 28792 z - 145538 z^2 + 374050 z^3 - 574998 z^4 + 551544 z^5\\&- 328166 z^6 + 113833 z^7 - 19178 z^8 + 704 z^9) + y^9 (-6561 + 96216 z - 598074 z^2 + 2006252 z^3 - 3969623 z^4 \\&+ 4828260 z^5 - 3670950 z^6 + 1713820 z^7 - 448924 z^8 + 49872 z^9) + y^8 (3361 - 62011 z + 494076 z^2 \\&- 2075590 z^3 + 5157019 z^4 - 8018097 z^5 + 8000348 z^6 - 5125514 z^7 + 2032884 z^8 - 448924 z^9 + 41296 z^{10})\\&+ 2 y^7 (-500 + 12419 z - 137577 z^2 + 734318 z^3 - 2271456 z^4 + 4429489 z^5 - 5635698 z^6 + 4719742 z^7 \\&- 2562757 z^8 + 856910 z^9 - 156690 z^{10} + 11584 z^{11}) + y^4 z^2 (2244 - 31624 z + 242798 z^2 - 1036852 z^3\\&+ 2692286 z^4 - 4542912 z^5 + 5157019 z^6 - 3969623 z^7 + 2031803 z^8 - 652809 z^9 + 116054 z^{10} - 8560 z^{11}\\&+ 176 z^{12}) + y^5 z (468 - 21768 z + 204538 z^2 - 1036852 z^3 + 3244920 z^4 -6575600 z^5 + 8858978 z^6\\&- 8018097 z^7 + 4828260 z^8 - 1859997 z^9 + 420138 z^{10} - 46660 z^{11} + 1816 z^{12}) + 2 y^6 (66 - 2724 z \\&+ 49908 z^2 - 346959 z^3 + 1346143 z^4 - 3287800 z^5 + 5273177 z^6 - 5635698 z^7 + 4000174 z^8 - 1835475 z^9\\&+ 509962 z^{10} - 74854 z^{11} + 4224 z^{12})) H(2, y) + 9 (-1 + y)^4 (-1 + z)^4 (-1 + y + z)^2 (y + z)^6 (4 + 56 y^3+ 34 z\\&- 101 z^2 + 56 z^3 + y^2 (-101 + 84 z) + y (34 - 76 z + 84 z^2)) H(2, y)^2 + H(0, z) (8 (-1 + z)^2 z (-1 + y + z)^2\\&\times (y + z)^6 (12 (-1 + z)^2 z + y^6 (12 - 33 z + 4 z^2) + 2 y^5 (-54 + 195 z - 189 z^2 + 82 z^3) + y^4 (336 - 1341 z\\&+ 1662 z^2 - 799 z^3 + 40 z^4) - 2 y^3 (240 - 1065 z + 1516 z^2 - 805 z^3 + 80 z^4) + y^2 (324 - 1620 z + 2790 z^2\\&- 1955 z^3 + 444 z^4) + 2 y (-42 + 231 z - 511 z^2 + 556 z^3 - 306 z^4 + 72 z^5)) + 48 (-1 + y)^4 y (-1 + z)^4\\&\times (-1 + y + z)^2 (y + z)^6 (6 + 8 y^2 - 6 z + 3 y (-5 + 4 z)) H(1, y) - 48 (-1 + y)^4 (-1 + z)^4 (-1 + y + z)^2\\&\times (y + z)^6 (8 y^3 + 3 y^2 (-5 + 4 z) + 6 y (1 + z - 4 z^2) - 3 z (4 - 15 z + 12 z^2)) H(2, y)) + H(1, z) \end{aligned}$$
$$\begin{aligned}&\times (8 (-1 + y + z) (144 y^{15} z + 6 (-1 + z)^5 z^6 (3 - 2 z + 2 z^2) + 4 y^{14} (34 - 397 z + 567 z^2- 176 z^3 + 44 z^4)\\&+ y^{13} (-866 + 8100 z - 20569 z^2 + 19018 z^3 - 7767 z^4 + 1652 z^5) + 2 y (-1 + z)^4 z^5 (-216 + 221 z + 222 z^2\\&- 456 z^3 + 370 z^4 - 234 z^5 + 72 z^6) + y^{12} (2374 - 23858 z + 83917 z^2 - 129245 z^3 + 97321 z^4\\&- 38669 z^5 + 7008 z^6) + y^2 (-1 + z)^3 z^4 (6 - 780 z - 2588 z^2 + 13184 z^3 - 18942 z^4 + 14294 z^5\\&- 6479 z^6 + 1452 z^7) + y^{11} (-3622 + 43744 z - 199491 z^2 + 436042 z^3 - 501379 z^4 + 321120 z^5\\&- 113638 z^6 + 17512 z^7) + y^{10} (3290 - 50918 z + 300333 z^2 - 878721 z^3 + 1407853 z^4 - 1304275 z^5\\&+ 713376 z^6 - 217490 z^7 + 28280 z^8) - y^3 (-1 + z)^2 z^3 (1584 - 2338 z - 14788 z^2 + 72720 z^3 - 149820 z^4\\&+ 171732 z^5 - 117066 z^6 + 45939 z^7 - 8478 z^8 + 160 z^9) + 2 y^9 (-863 + 18146 z - 145902 z^2 + 567991 z^3 \\&- 1216836 z^4+ 1534256 z^5 - 1178239 z^6 + 547769 z^7 - 141466 z^8 + 15288 z^9) + 2 y^8 (213 - 6663 z\\&+ 89049 z^2 - 480126 z^3 + 1360821 z^4 - 2265678 z^5 + 2330148 z^6 - 1502619 z^7 + 590049 z^8\\&- 126886 z^9 + 11116 z^{10}) + 2 y^7 (3 + 76 z - 31201 z^2 + 259264 z^3 - 985699 z^4 + 2156109 z^5\\&- 2918981 z^6 + 2511740 z^7 - 1366047 z^8 + 447153 z^9 - 77957 z^{10} + 5324 z^{11})\\&+ y^4 z^2 (-6 + 5026 z + 3058 z^2 - 165362 z^3 + 688552 z^4 - 1444642 z^5 + 1850424 z^6 - 1531142 z^7\\&+ 816755 z^8 - 264717 z^9 + 44437 z^{10} - 2423 z^{11} + 40 z^{12}) + y^5 z (-432 - 66 z + 18020 z^2 - 196646 z^3\\&+ 926280 z^4 - 2346594 z^5 + 3574134 z^6 - 3448086 z^7 + 2127944 z^8 - 811205 z^9 + 172740 z^{10}\\&- 16485 z^{11} + 540 z^{12}) + 2 y^6 (-9 + 845 z + 4861 z^2 - 81055 z^3 + 437656 z^4 - 1299435 z^5\\ \end{aligned}$$
$$\begin{aligned}&+ 2341652 z^6 - 2665679 z^7 + 1940166 z^8 - 884963 z^9 + 236428 z^{10} - 31919 z^{11} + 1596 z^{12}))\\&+ 48 (-1 + y)^4 (-1 + z)^4 (-1 + y + z)^2 (y + z)^6 (-4 + 28 y^3 + 18 z - 21 z^2 + 8 z^3 + 4 y^2 (-8 + 5 z)\\&+ 2 y (5 - 10 z + 2 z^2)) H(2, y) - 144 (-1 + y)^4 (-1 + z)^4 (-1 + y + z)^2 (y + z)^6 (12 y^3 + y^2 (-15 + 8 z)\\&+ y (4 - 8 z + 8 z^2) + z (4 - 15 z + 12 z^2)) H(3, y)) + 6 (-1 + y)^4 (-1 + z)^4 (-1 + y + z)^2 (y + z)^6 \\&\times (46 + 704 y^3 - 112 z + 254 z^2 - 192 z^3 + y^2 (-717 + 404 z) - 2 y (-21 + 11 z + 88 z^2)) H(0, 0, y)\\&- 6 (-1 + y)^4 (-1 + z)^4 (-1 + y + z)^2 (y + z)^6 (-46 + 192 y^3 - 42 z + 717 z^2 - 704 z^3\\&+ 2 y^2 (-127 + 88 z) + y (112 + 22 z - 404 z^2)) H(0, 0, z) - 96 (-1 + y)^4 (-1 + 4 y) (-1 + z)^4\\&\times (-1 + y + z)^2 (y + z)^6 (2 + 2 y^2 + 2 y (-2 + z) - 2 z + z^2) H(0, 1, y) - 144 (-1 + y)^4\\&\times y (-1 + z)^4 (-1 + y + z)^2 (y + z)^6 (4 + 12 y^2 - 4 z + y (-15 + 8 z)) H(0, 1, z)\\&+ 48 (-1 + y)^4 (-1 + z)^4 (-1 + y + z)^2 (y + z)^6 (52 y^3 + y^2 (-81 + 40 z) - 2 (2 - 2 z + z^2)\\&+ 4 y (9 - 8 z + 2 z^2)) H(0, 2, y) - 144 (-1 + y)^4 y (-1 + z)^4 (-1 + y + z)^2 (y + z)^6 (4 + 12 y^2 - 4 z\\&+ y (-15 + 8 z)) H(1, 0, y) - 48 (-1 + y)^4 y (-1 + z)^4 (-1 + y + z)^2 (y + z)^6 (6 + 8 y^2 - 6 z \\&+ 3 y (-5 + 4 z)) H(1, 0, z) + 48 (-1 + y)^4 (-1 + z)^4 (-1 + y + z)^2 (y + z)^6 (20 y^3 + y^2 (-9 + 8 z)\\&+ 2 (2 - 2 z + z^2) - 4 y (3 - 2 z + 2 z^2)) H(1, 1, y) + 6 (-1 + y)^4 (-1 + z)^4 (-1 + y + z)^2 (y + z)^6 \\&\times (56 y^3 + y^2 (63 - 156 z) - 18 y (3 - 10 z + 14 z^2) - 3 (4 + 34 z - 101 z^2 + 56 z^3)) H(1, 1, z)\\&- 96 (-1 + y)^4 y (-1 + z)^4 (-1 + y + z)^2 (y + z)^6 (3 + 14 y^2 - 3 z + 3 y (-5 + 2 z)) H(1, 2, y) \\&+ 48 (-1 + y)^4 (-1 + z)^4 (-1 + y + z)^2 (y + z)^6 (36 y^3 + 3 y^2 (-15 + 8 z) + z (-6 + 15 z - 8 z^2)\\&- 6 y (-2 + z + 2 z^2)) H(2, 0, y) - 48 (-1 + y)^4 (-1 + z)^4 (-1 + y + z)^2 (y + z)^6 (36 y^3\\&+ 16 y (-1 + z)^2 + 4 (-1 + z)^2 (-1 + 4 z) + y^2 (-47 + 32 z)) H(2, 1, y) + 6 (-1 + y)^4 (-1 + z)^4\\&\times (-1 + y + z)^2 (y\\ \end{aligned}$$
$$\begin{aligned}&+ z)^6 (-76 + 184 y^3 + 170 z - 241 z^2 + 184 z^3 + y^2 (-241 + 36 z) + 2 y (85 - 94 z + 18 z^2)) H(2, 2, y) \\&- 144 (-1 + y)^4 (-1 + z)^4 (-1 + y + z)^2 (y + z)^6 (12 y^3 + y^2 (-15 + 8 z) + y (4 - 8 z + 8 z^2)\\&\quad + z (4 - 15 z + 12 z^2)) H(3, 2, y)\Bigg \}\Big /\Big (48 (-1 + y)^4 y (-1 + z)^4 z (-1 + y + z)^2 (y + z)^6\Big );\\ \mathcal {A}_{6;n_{f}^{2}}^{(2)}&= \frac{1}{18} ~ \mathcal {A}_{0} ;\\ \mathcal {A}_{6;C_{A}C_{F}}^{(2)}&= \Bigg \{-2 (-1 + y) (-1 + z) (y + z) (1152 y^{13} z - 9 (-1 + z)^5 z^5 (90 - 94 z + 41 z^2)\\&+ 3 y^{12} (-123 - 2483 z + 4229 z^2 - 1283 z^3 + 428 z^4) + 3 y (-1 + z)^4 z^4 (1350 - 5784 z + 5943 z^2 - 1088 z^3\\&- 947 z^4 + 384 z^5) + 3 y^{11} (897 + 5004 z - 25436 z^2 + 30556 z^3 - 16597 z^4 + 4808 z^5) + 3 y^2 (-1 + z)^3 z^3\\&\times (-2700 + 13740 z - 36361 z^2 + 35633 z^3 - 2149 z^4 - 12749 z^5 + 4229 z^6) + y^{10} (-8730 + 9231 z + 146355 z^2\\&- 412685 z^3 + 451131 z^4 - 253782 z^5 + 61568 z^6) + 2 y^9 (8100 - 47868 z - 594 z^2 + 355100 z^3 - 742645 z^4\\&+ 700596 z^5 - 341189 z^6 + 68500 z^7) - y^3 (-1 + z)^2 z^2 (-8100 + 99768 z - 310125 z^2 + 455122 z^3\\&- 249510 z^4 - 144438 z^5 + 240896 z^6 - 83970 z^7 + 3849 z^8) + y^8 (-18405 + 190647 z - 410874 z^2\\&- 280262 z^3 + 2163621 z^4 - 3406317 z^5 + 2683478 z^6 - 1092120 z^7 + 177144 z^8) + y^7 (12699 - 194892 z\\&+ 695613 z^2 - 809704 z^3 - 883105 z^4 + 3818004 z^5 - 4987759 z^6 + 3306568 z^7 - 1092120 z^8 + 137000 z^9)\\&+ y^6 (-4896 + 111537 z - 565908 z^2 + 1469879 z^3 - 1595836 z^4 - 916967 z^5 + 4424978 z^6 - 4987759 z^7 \\&+ 2683478 z^8 - 682378 z^9 + 61568 z^{10}) + y^4 z (4050 - 65520 z + 517761 z^2 - 1698158 z^3 + 2639853 z^4\\&- 1595836 z^5 - 883105 z^6 + 2163621 z^7 - 1485290 z^8 + 451131 z^9 - 49791 z^{10} + 1284 z^{11})\\&+ y^5 (810 - 33552 z + 257043 z^2 - 1175140 z^3 + 2639853 z^4 - 2346720 z^5 - 916967 z^6+ 3818004 z^7\\&- 3406317 z^8 + 1401192 z^9 - 253782 z^{10} + 14424 z^{11})) + 9 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6\\&\times (-27+ 612 y^4 + 7 z - 18 z^2 + 130 z^3 - 92 z^4 + 6 y^3 (-219 + 206 z) + 6 y^2 (127 - 251 z + 78 z^2)\\&- 3 y (11 - 102 z + 26 z^2 + 52 z^3)) H(0, y)^2 - 9 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6 (27 + 92 y^4\\&+ 33 z - 762 z^2 + 1314 z^3 - 612 z^4 + 26 y^3 (-5 + 6 z) + y^2 (18 + 78 z - 468 z^2) - y (7 + 306 z - 1506 z^2\\&+ 1236 z^3)) H(0, z)^2 - 9 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6 (-58 + 80 y^4 + 136 z + 27 z^2 - 185 z^3 \end{aligned}$$
$$\begin{aligned}&+ 80 z^4 + 5 y^3 (-37 + 68 z) + 3 y^2 (9 - 139 z + 112 z^2) + y (136 - 12 z - 417 z^2 + 340 z^3)) H(1, z)^2\\&+ H(0, y) (-12 (-1 + y)^2 y (-1 + y + z) (y + z)^6 (192 y^6 z + 4 y^5 z (-255 + 207 z - 64 z^2 + 16 z^3) \\&- 6 (-1 + z)^4 (1 + 18 z - 47 z^2 + 32 z^3) + 3 y (-1 + z)^3 (3 + 6 z + 242 z^2 - 344 z^3 + 134 z^4)\\&- y^2 (-1 + z)^2 (-63 - 1120 z + 692 z^2 + 644 z^3 - 824 z^4 + 208 z^5) + y^4 (27 + 2224 z - 3883 z^2\\&+ 2826 z^3 - 1250 z^4 + 248 z^5) - y^3 (75 + 2315 z - 5945 z^2 + 5649 z^3 - 2530 z^4 + 376 z^5 + 60 z^6))\\&- 72 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6 (56 y^4 - 3 y^2 (-7 + 9 z) + y^3 (-91 + 60 z)\\&+ y (20 - 36 z + 27 z^2 - 12 z^3) + 3 (-2 + 4 z - 3 z^2 + z^3)) H(1, z)) + H(1, y) (12 (-1 + y)^3 (-1 + z)^4\\&\times (-1 + y + z) (y + z)^6 (-406 + 388 y^5 + 1020 z - 1029 z^2 + 383 z^3 + y^4 (-1877 + 1092 z)\\&+ y^3 (3592 - 3873 z + 1116 z^2) + y (1814 - 3714 z + 3018 z^2 - 859 z^3) + y^2 (-3511 + 5475 z \\&- 3111 z^2 + 476 z^3)) + 72 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6 (2 + 24 y^4 - 4 z + 3 z^2 \\&- z^3 + 4 y^3 (-7 + 10 z) - 6 y^2 (2 + 3 z + 2 z^2) + y (14 - 3 z^2 + 4 z^3)) H(1, z))\\&- 6 (-1 + y + z) (384 y^{15} z + (-1 + z)^5 z^6 (-726 + 1882 z - 2105 z^2 + 776 z^3) + 8 y^{14} (97\\&- 739 z + 1077 z^2 - 452 z^3 + 113 z^4) + y^{13} (-5985 + 40168 z - 92560 z^2 + 89128 z^3 - 40267 z^4\\&+ 8364 z^5) + y (-1 + z)^4 z^5 (2964 - 19836 z + 41602 z^2 - 41559 z^3 + 20360 z^4 - 4376 z^5 + 384 z^6)\\&+ y^{12} (20167 - 150791 z + 451180 z^2 - 659196 z^3 + 502581 z^4 - 202437 z^5 + 35424 z^6) \\&+ 2 y^2 (-1 + z)^3 z^4 (-6765 + 42879 z - 127932 z^2 + 212727 z^3 - 204354 z^4 + 112598 z^5\\&- 33356 z^6 + 4308 z^7) + 2 y^{11} (-19473 + 173943 z - 646524 z^2 + 1262820 z^3 - 1387944 z^4+ 876471 z^5\\&- 304141 z^6 + 45232 z^7) + 2 y^{10} (23690 - 260707 z + 1196939 z^2 - 2976262 z^3 + 4350991 z^4 - 3849912 z^5 \end{aligned}$$
$$\begin{aligned}&+ 2048644 z^6 - 608211 z^7 + 77132 z^8) - 2 y^3 (-1 + z)^2 z^3 (-4252 + 81656 z - 390703 z^2 + 946461 z^3\\&- 1380495 z^4 + 1270200 z^5 - 730084 z^6 + 245894 z^7 - 40948 z^8 + 1808 z^9) + y^9 (-37381 + 518516 z\\&- 2983546 z^2 + 9301958 z^3 - 17356961 z^4 + 20206452 z^5 - 14838192 z^6 + 6708682 z^7 - 1702288 z^8 \\&+ 183528 z^9) + y^8 (18775 - 338839 z + 2538420 z^2 - 9955302 z^3 + 23235465 z^4 - 34337223 z^5\\&+ 32931038 z^6 - 20432684 z^7 + 7885302 z^8 - 1702288 z^9 + 154264 z^{10})\\&+ 2 y^7 (-2756 + 69365 z - 731925 z^2 + 3664120 z^3 - 10625532 z^4 + 19591238 z^5 - 23845782 z^6\\&+ 19305676 z^7 - 10216342 z^8 + 3354341 z^9 - 608211 z^{10} + 45232 z^{11}) \\&+ y^4 z^2 (13530 - 180320 z + 1309202 z^2 - 5314260 z^3 + 13155096 z^4 - 21251064 z^5\\&+ 23235465 z^6 - 17356961 z^7 + 8701982 z^8 - 2775888 z^9 + 502581 z^{10} - 40267 z^{11}\\&+ 904 z^{12}) + y^5 z (2964 - 126348 z + 1116534 z^2 - 5314260 z^3 + 15703800 z^4 - 30293056 z^5\\&+ 39182476 z^6 - 34337223 z^7 + 20206452 z^8 - 7699824 z^9 + 1752942 z^{10} - 202437 z^{11}\\&+ 8364 z^{12}) + 2 y^6 (363 - 15846 z + 276864 z^2 - 1809523 z^3 + 6577548 z^4 - 15146528 z^5\\&+ 23154650 z^6 - 23845782 z^7 + 16465519 z^8 - 7419096 z^9 +2048644 z^{10} - 304141 z^{11}\\&+ 17712 z^{12})) H(2, y) - 9 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6 (-58 + 80 y^4 + 136 z + 27 z^2\\&- 185 z^3 + 80 z^4 + 5 y^3 (-37 + 68 z) + 3 y^2 (9 - 139 z + 112 z^2) + y (136 - 12 z - 417 z^2 + 340 z^3))\\&\times H(2, y)^2 + H(0, z) (12 (-1 + z)^2 z (-1 + y + z) (y + z)^6 (-3 (-1 + z)^3 (2 + 9 z)\\&+ 2 y^7 (96 - 201 z + 104 z^2) + 2 y^6 (-525 + 1119 z - 620 z^2 + 30 z^3) \\&- 4 y^5 (-597 + 1257 z - 625 z^2 - 94 z^3+ 62 z^4) - y (-1 + z)^2(-84 - 159 z + 760 z^2 -636 z^3 + 192 z^4) \end{aligned}$$
$$\begin{aligned}&+ y^2 (-678 + 699 z + 2869 z^2 - 5945 z^3 + 3883 z^4 - 828 z^5) - 2 y^4 (1443 - 2829 z + 710 z^2 + 1265 z^3 \\&- 625 z^4 + 32 z^5)+ y^3 (1944 - 3165 z - 1860 z^2 + 5649 z^3 - 2826 z^4 + 256 z^5)) - 72 (-1 + y)^4 (-1 + z)^4\\&\times (-1 + y + z) (y + z)^6 (-2 + 32 y^4 + 4 z - 3 z^2 + z^3 + y^3 (-93 + 68 z) \\&+ 3 y^2 (29 - 39 z + 16 z^2) - y (24 - 36 z + 15 z^2 + 4 z^3)) H(1, y) + 288 (-1 + y)^4 (-1 + z)^4\\&\times (-1 + y + z) (y + z)^6 (1 + 8 y^4 - 4 z - 6 z^2 + 23 z^3 - 14 z^4 + 4 y^3 (-6 + 5 z)\\&+ 12 y^2 (2 - 3 z + z^2) + y (-9 + 18 z + 3 z^2 - 16 z^3)) H(2, y)) + H(1, z) (-6 (-1 + y + z)\\&\times (384 y^{15} z + (-1 + z)^5 z^6 (86 - 122 z + 97 z^2) + 8 y^{14} (97 - 739 z + 1077 z^2\\&- 452 z^3 + 113 z^4) + y^{13} (-5219 + 36152 z - 84156 z^2 + 80352 z^3 - 35693 z^4 + 7412 z^5)\\&+ y (-1 + z)^4 z^5 (-1908 + 2348 z - 286 z^2 - 1305 z^3 + 1608 z^4 - 1272 z^5 + 384 z^6)\\&+ y^{12} (15045 - 117921 z + 362964 z^2 - 532604 z^3 + 400231 z^4 - 158267 z^5 + 27480 z^6)\\&+ 2 y^2 (-1 + z)^3 z^4 (-675 - 195 z - 1902 z^2 + 12975 z^3 - 20676 z^4 + 17018 z^5 - 8414 z^6 \\&+ 1980 z^7) + 2 y^{11} (-12039 + 115335 z - 450060 z^2 + 899424 z^3 - 987042 z^4 + 612507 z^5\\&- 208045 z^6 + 30304 z^7) + 2 y^{10} (11498 - 141313 z + 701873 z^2 - 1830608 z^3 + 2724693 z^4\\&- 2395960 z^5 + 1248128 z^6 - 359939 z^7 + 43932 z^8) - 2 y^3 (-1 + z)^2 z^3 (3868 - 2404 z\\&- 34723 z^2 + 117005 z^3 - 200991 z^4 + 214578 z^5 - 145420 z^6 + 58736 z^7 - 11368 z^8 + 256 z^9)\\&+ y^9 (-12895 + 213812 z - 1415134 z^2 + 4813534 z^3 - 9392031 z^4 + 11059916 z^5 - 8020592 z^6 + 3525722 z^7\\&- 858756 z^8 + 87192 z^9) + y^8 (3685 - 89137 z + 912288 z^2 - 4186350 z^3 + 10584771 z^4\\&- 16190181 z^5 + 15575102 z^6 - 9479600 z^7 + 3525138 z^8 - 718540 z^9 + 59752 z^{10})\\&+ 2 y^7 (-112 + 5193 z - 179561 z^2 + 1190012 z^3 - 3904772 z^4 + 7681554 z^5 - 9620890 z^6 \\&+ 7790928 z^7 - 4023410 z^8 + 1256653 z^9 - 210091 z^{10} + 13920 z^{11})\\&+ y^4 z^2 (1350 + 16400 z + 21642 z^2 - 611924 z^3 + 2286652 z^4 - 4384532 z^5 + 5218711 z^6 \\&- 4097291 z^7 + 2122526 z^8 - 683628 z^9 + 116791 z^{10} - 6825 z^{11} + 128 z^{12})\\&+ y^5 z (-1908 - 10644 z + 125622 z^2 - 840744 z^3 + 3311496 z^4 - 7624456 z^5 + 10838140 z^6\\&- 9884853 z^7 + 5831340 z^8 - 2153460 z^9 + 452070 z^{10} - 43743 z^{11} + 1524 z^{12}) \end{aligned}$$
$$\begin{aligned}&+ 2 y^6 (-43 + 3050 z + 40106 z^2 - 411629 z^3 + 1786766 z^4 - 4630398 z^5 + 7634856 z^6\\&- 8152400 z^7 + 5636279 z^8 - 2461502 z^9 + 635000 z^{10} - 83925 z^{11} + 4224 z^{12}))\\&- 288 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6 (4 y^3 + 4 y^4 + 3 (-1 + z) z^2 \\&- 3 y^2 (6 - 7 z + 6 z^2) - 2 y (-5 + 9 z - 12 z^2 + 6 z^3)) H(2, y) + 432 (-1 + y)^4 (-1 + z)^4\\&\times (-1 + y + z)^2 (y + z)^6 (12 y^3 + y^2 (-15 + 8 z) + y (4 - 8 z + 8 z^2) \\&+ z (4 - 15 z + 12 z^2)) H(3, y)) - 18 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6 (-27 + 612 y^4 + 7 z\\&- 18 z^2 + 130 z^3 - 92 z^4 + 6 y^3 (-219 + 206 z) + 6 y^2 (127 - 251 z + 78 z^2) - 3 y (11 - 102 z\\&+ 26 z^2 + 52 z^3)) H(0, 0, y) + 18 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6 (27 + 92 y^4 + 33 z\\&- 762 z^2 + 1314 z^3 - 612 z^4 + 26 y^3 (-5 + 6 z) + y^2 (18 + 78 z - 468 z^2) - y (7 + 306 z - 1506 z^2\\&+ 1236 z^3)) H(0, 0, z) + 144 (-1 + y)^4 y (-1 + z)^4 (-1 + y + z) (y + z)^6 (16 y^3 + y^2 (-41 + 12 z)\\&- 2 (7 - 6 z + 3 z^2) + 3 y (13 - 9 z + 4 z^2)) H(0, 1, y) + 72 (-1 + y)^4 (-1 + z)^4 (-1 + y + z)^2 (y + z)^6 \\&\times (2 + 64 y^3 - 2 z + z^2 + 8 y^2 (-9 + 5 z) - 2 y (-6 + 7 z + 2 z^2)) H(0, 1, z) - 72 (-1 + y)^4 \\&\times (-1 + z)^4 (-1 + y + z) (y + z)^6 (104 y^4 + 2 (-1 + z)^3 (-1 + 4 z) + y^3 (-245 + 148 z) \\&+ 3 y^2 (65 - 77 z + 28 z^2) + 8 y (-7 + 12 z - 9 z^2 + 2 z^3)) H(0, 2, y) + 72 (-1 + y)^4 (-1 + z)^4\\&\times (-1 + y + z) (y + z)^6 (56 y^4 - 3 y^2 (-7 + 9 z) + y^3 (-91 + 60 z) + y (20 - 36 z + 27 z^2 - 12 z^3)\\&+ 3 (-2 + 4 z - 3 z^2 + z^3)) H(1, 0, y) + 72 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6 (-2 + 32 y^4 + 4 z\\&- 3 z^2 + z^3 + y^3 (-93 + 68 z) + 3 y^2 (29 - 39 z + 16 z^2) - y (24 - 36 z + 15 z^2 + 4 z^3)) H(1, 0, z)\\&- 216 (-1 + y)^4 y (-1 + z)^4 (-1 + y + z) (y + z)^6 (6 + 8 y^3 + 4 z - 2 z^2 + y^2 (-13 + 28 z)\\&+ y (-1 - 27 z + 4 z^2)) H(1, 1, y) + 18 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6 (-50 + 16 y^4\\&+ 120 z + 39 z^2 - 189 z^3 + 80 z^4 + y^3 (-253 + 356 z) + y^2 (327 - 741 z + 528 z^2) + y (-40 + 228 z\\&- 549 z^2 + 356 z^3)) H(1, 1, z) + 72 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6 (2 + 24 y^4 - 4 z\\&+ 3 z^2 - z^3 + 4 y^3 (-7 + 10 z) - 6 y^2 (2 + 3 z + 2 z^2) + y (14 - 3 z^2 + 4 z^3)) H(1, 2, y)\\&- 288 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6 (-1+ 14 y^4 + 9 z - 24 z^2 + 24 z^3 \end{aligned}$$
$$\begin{aligned}&- 8 z^4 + y^3 (-23 + 16 z) - 3 y^2 (-2 + z + 4 z^2) + y (4 - 18 z + 36 z^2 - 20 z^3))\\&\times H(2, 0, y) + 144 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6 (4 + 32 y^4 - 38 z + 87 z^2 - 77 z^3 + 24 z^4\\&+ y^3 (-75 + 68 z) + 3 y^2 (19 - 39 z + 20 z^2) + y (-18 + 84 z - 111 z^2 + 44 z^3)) H(2, 1, y)\\&- 18 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6 (90 + 176 y^4 - 280 z + 381 z^2 - 367 z^3 + 176 z^4\\&+ y^3 (-367 + 12 z) - 3 y^2 (-127 + 45 z + 48 z^2) + y (-280 + 396 z - 135 z^2 + 12 z^3)) H(2, 2, y) \\&+ 432 (-1 + y)^4 (-1 + z)^4 (-1 + y + z)^2 (y + z)^6 (12 y^3 + y^2 (-15 + 8 z) + y (4 - 8 z + 8 z^2)\\&+ z (4 - 15 z + 12 z^2)) H(3, 2, y)\Bigg \}\Big /\Big (144 (-1 + y)^4 y (-1 + z)^4 z (-1 + y + z)^2 (y + z)^6\Big );\\ \mathcal {A}_{6;C_{A}n_{f}}^{(2)}&= \Bigg \{(-1 + y) (-1 + z) (y + z) (864 y^{12} z + 7 (-1 + z)^4 z^5 (2 - 2 z + z^2) + y^{11} (7 - 3181 z + 2877 z^2 + 3053 z^3\\&- 1028 z^4)+ y (-1 + z)^3 z^4 (-70 + 138 z + 447 z^2 - 697 z^3 - 589 z^4 + 864 z^5) - 2 y^{10} (21 - 1831 z \\&+ 3460 z^2 + 8127 z^3 - 12227 z^4 + 3314 z^5) + y^9 (112 - 93 z - 3293 z^2 + 54841 z^3 - 123339 z^4 + 85304 z^5\\&- 18716 z^6) + y^2 (-1 + z)^2 z^3 (140 - 770 z - 1605 z^2 + 8180 z^3 - 8502 z^4 - 1166 z^5 + 2877 z^6)\\&- y^8 (168 + 2705 z - 24018 z^2 + 117638 z^3 - 307100 z^4 + 350637 z^5 - 170234 z^6 + 30204 z^7)+ y^7 (147 + 1554 z\\&- 26467 z^2 + 142908 z^3 - 438373 z^4 + 710452 z^5 - 567495 z^6 + 212662 z^7- 30204 z^8)+ y^6 (-70 + 177 z\\&+ 10620 z^2 - 97217 z^3 + 373368 z^4 - 794957 z^5 + 925784 z^6- 567495 z^7 + 170234 z^8 - 18716 z^9)+ y^3 z^2 (140\\&+ 376 z - 7503 z^2 + 37294 z^3 - 97217 z^4+ 142908 z^5 - 117638 z^6 + 54841 z^7 - 16254 z^8 + 3053 z^9) \end{aligned}$$
$$\begin{aligned}&+ y^5 (14 - 348 z + 75 z^2 + 37294 z^3 - 197115 z^4 + 514818 z^5 - 794957 z^6 + 710452 z^7 - 350637 z^8 + 85304 z^9\\&- 6628 z^{10}) + y^4 z (70 - 1050 z - 7503 z^2 + 62552 z^3 - 197115 z^4 + 373368 z^5 - 438373 z^6 + 307100 z^7\\&- 123339 z^8 + 24454 z^9 - 1028 z^{10})) + 12 (-1 + y)^4 (y + z)^6 (72 y^5 z - (-1 + z)^5 (2 - 2 z + z^2)\\&+ y^4 z (-171 + 177 z - 8 z^2 + 2 z^3) + y^3 (-1 + z)^2 (-1 + 150 z - 33 z^2 + 12 z^3) + 3 y^2 (-1 + z)^3 \\&\times (-1 + 25 z - 33 z^2 + 22 z^3) + y (-1 + z)^4 (-4 + 30 z - 81 z^2 + 64 z^3)) H(0, y) + 27 (-1 + y)^4 (-1+ z)^4 z (-1\\&+ y + z) (y + z)^6 (3 - 12 z + 10 z^2 + y (-3 + 6 z)) H(0, y)^2 + 27 (-1 + y)^4 y (3 + 10 y^2 + 6 y (-2 + z) - 3 z)\\&\times (-1 + z)^4 (-1 + y + z) (y + z)^6 H(0, z)^2 - 108 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6 \\&\times (10 y^3 + 6 y^2 (-2 + z) + y (3 - 6 z + 6 z^2) + z (3 - 12 z + 10 z^2)) H(1, z)^2 + H(1, y) (12 (-1 + y)^4 \\&\times (-1 + z)^4 (y + z)^6 (22 y^4 + z (-1 + 3 z) + 2 y^3 (-29 + 8 z) - 3 y (7 - 6 z + 3 z^2)\\&+ 3 y^2 (19 - 13 z + 6 z^2)) - 72 (-1 + y)^4 y (3 + 10 y^2 + 6 y (-2 + z) - 3 z) (-1 + z)^4 (-1 + y + z)(y + z)^6\\&\times H(1, z)) + 6 (144 y^{15} z - (-1 + z)^5 z^6 (-2 + 44 z - 73 z^2 + 44 z^3) - 2 y^{14} (22 + 371 z - 477 z^2\\&- 80 z^3 + 20 z^4) + y^{13} (293 + 1168 z - 5070 z^2 + 2496 z^3 + 821 z^4 - 140 z^5) + y (-1 + z)^4 z^5 \\&\times (-24 + 332 z - 904 z^2 + 1005 z^3 - 360 z^4 - 166 z^5 + 144 z^6) + y^{12} (-849 + 873 z + 9576 z^2\\&- 16678 z^3 + 5423 z^4 + 311 z^5 + 192 z^6) + 6 y^2 (-1 + z)^3 z^4 (5 - 169 z + 700 z^2 - 1162 z^3 + 833 z^4 \\&+ 15 z^5 - 368 z^6 + 159 z^7) + 2 y^{11} (696 - 3138 z - 1425 z^2 + 18410 z^3 - 21716 z^4 + 10176 z^5\\&- 3835 z^6 + 976 z^7) + 2 y^{10} (-700 + 5626 z - 9744 z^2 - 13652 z^3 + 51737 z^4 - 54675 z^5 + 33289 z^6\\&- 13437 z^7 + 2420 z^8) + 2 y^3 (-1 + z)^2 z^3 (-168 + 1335 z - 5622 z^2 + 12199 z^3 - 12840 z^4 + 3543 z^5\\&+ 5796 z^6 - 5603 z^7 + 1408 z^8 + 80 z^9) + y^9 (869 - 11156 z + 40020 z^2 - 28260 z^3 - 100851 z^4 + 231456 z^5\\&- 227034 z^6 + 134608 z^7 - 45724 z^8 + 6360 z^9) + y^8 (-313 + 6709 z - 39528 z^2 + 82844 z^3 - 7079 z^4\\&- 224019 z^5 + 385714 z^6 - 333886 z^7 + 169290 z^8 - 45724 z^9 + 4840 z^{10})\\&+ 2 y^7 (27 - 1188 z + 11322 z^2 - 42860 z^3 + 61782 z^4 + 15764 z^5 - 162079 z^6 + 229116 z^7 - 166943 z^8 \end{aligned}$$
$$\begin{aligned}&+ 67304 z^9 - 13437 z^{10} + 976 z^{11}) + y^5 z (-24 + 1104 z - 16920 z^2 + 80478 z^3 - 172200 z^4\\&+ 157568 z^5 + 31528 z^6 - 224019 z^7 + 231456 z^8 - 109350 z^9 + 20352 z^{10} + 311 z^{11} - 140 z^{12})\\&+ y^4 z^2 (-30 + 3342 z - 24582 z^2 + 80478 z^3 - 141088 z^4 + 123564 z^5 - 7079 z^6 - 100851 z^7\\&+ 103474 z^8 - 43432 z^9 + 5423 z^{10} + 821 z^{11} - 40 z^{12}) + 2 y^6 (-1 + 214 z - 3666 z^2 + 24778 z^3\\&- 70544 z^4 + 78784 z^5 + 23768 z^6 - 162079 z^7 + 192857 z^8 - 113517 z^9 + 33289 z^{10} - 3835 z^{11}\\&+ 96 z^{12})) H(2, y) - 108 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6 (10 y^3 + 6 y^2 (-2 + z)\\&+ y (3 - 6 z + 6 z^2) + z (3 - 12 z + 10 z^2)) H(2, y)^2 + H(0, z) (12 (-1 + z)^4 (y + z)^6 (2 - 4 z + 3 z^2 - z^3\\&+ y^7 (-1 + 64 z) + y^6 (7 - 337 z + 66 z^2) + y^5 (-22 + 738 z - 297 z^2 + 12 z^3) + y^3 (-45 + 584 z - 591 z^2\\&+ 228 z^3 - 8 z^4) + y^4 (40 - 866 z + 570 z^2 - 57 z^3 + 2 z^4) + y^2 (31 - 225 z + 333 z^2 - 334 z^3 + 177 z^4)\\&+ y (-12 + 46 z - 84 z^2 + 152 z^3 - 171 z^4 + 72 z^5)) - 72 (-1 + y)^4 y (3 + 10 y^2 + 6 y (-2 + z) - 3 z) \\&\times (-1 + z)^4 (-1 + y + z) (y + z)^6 H(1, y) + 72 (-1 + y)^4 y (3 + 10 y^2 + 6 y (-2 + z) - 3 z) (-1 + z)^4\\&\times (-1 + y + z) (y + z)^6 H(2, y)) + H(1, z) (6 (144 y^{15} z + (-1 + z)^5 z^6 (2 - 2 z + z^2) \\&- 2 y^{14} (22 + 371 z - 477 z^2 - 80 z^3 + 20 z^4) + y^{13} (293 + 1168 z - 5070 z^2 + 2496 z^3 + 821 z^4\\&- 140 z^5) + y (-1 + z)^4 z^5 (-24 + 78 z - 16 z^2 - 225 z^3 + 400 z^4 - 342 z^5 + 144 z^6) + y^{12}\\&\times (-843 + 831 z + 9720 z^2 - 16954 z^3 + 5717 z^4 + 149 z^5 + 228 z^6) + 2 y^2 (-1 + z)^3 z^4\\&\times (15 - 186 z + 305 z^2 + 667 z^3 - 2514 z^4 + 3319 z^5 - 2176 z^6 + 609 z^7) + 2 y^{11} \\&\times (683 - 3014 z - 1956 z^2 + 19678 z^3 - 23503 z^4 + 11652 z^5 - 4496 z^6 + 1100 z^7) \\&+ 2 y^{10} (-678 + 5313 z - 8022 z^2 - 18773 z^3 + 60879 z^4 - 64750 z^5 + 39999 z^6 - 15912 z^7 + 2808 z^8)\\&- 2 y^3 (-1 + z)^2 z^3 (168 - 900 z + 2040 z^2 + 85 z^3 - 10206 z^4 + 22176 z^5 - 23052 z^6 + 12257 z^7\\&- 2704 z^8 + 8 z^9) + y^9 (833 - 10292 z + 33702 z^2 - 4660 z^3 - 153421 z^4 + 305336 z^5 - 293084 z^6\\&+ 170960 z^7 - 56910 z^8 + 7824 z^9) + y^8 (-299 + 6023 z - 32496 z^2 + 49134 z^3 + 86751 z^4 - 389079 z^5\\&+ 574814 z^6 - 474284 z^7 + 234114 z^8 - 62510 z^9 + 6680 z^{10}) + 2 y^7 (26 - 1040 z + 8961 z^2- 27672 z^3 + 8010 z^4 \\&+ 134028 z^5 - 332223 z^6 + 391604 z^7 - 268514 z^8 + 106908 z^9 - 22068 z^{10}+ 1764 z^{11})+ y^4 z^2 (-30 + 2672 z \\&- 15902 z^2+ 33612 z^3+ 1816 z^4 - 152124 z^5 + 346211 z^6 - 406001 z^7 + 279114 z^8 - 108142 z^9 + 19425 z^{10}\\&- 655 z^{11} + 4 z^{12})+ y^5 z (-24 + 822 z - 11768 z^2 + 45164 z^3 - 41376 z^4- 142688 z^5 + 485144 z^6 - 685563 z^7 \end{aligned}$$
$$\begin{aligned}&\quad + 546704 z^8- 249740 z^9 + 58512 z^{10} - 5199 z^{11} + 156 z^{12}) + 2 y^6 (-1 + 187 z - 2784 z^2 + 16395 z^3 - 31152 z^4\\&\quad - 31320 z^5 + 222248 z^6 - 400783 z^7 + 385277 z^8 - 215282 z^9 + 66695 z^{10} - 9876 z^{11} + 540 z^{12}))\\&\quad + 72 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6 (10 y^3 + 6 y^2 (-2 + z) + y (3 - 6 z + 6 z^2) + z (3 - 12 z + 10 z^2)) \\&\quad \times H(2, y)) - 54 (-1 + y)^4 (-1 + z)^4 z (-1 + y + z) (y + z)^6 (3 - 12 z + 10 z^2 + y (-3 + 6 z)) H(0, 0, y)\\&\quad - 54 (-1 + y)^4 y (3 + 10 y^2 + 6 y (-2 + z) - 3 z) (-1 + z)^4 (-1 + y + z) (y + z)^6 H(0, 0, z) \\&\quad + 72 (-1 + y)^4 y (3 + 10 y^2 + 6 y (-2 + z) - 3 z) (-1 + z)^4 (-1 + y + z) (y + z)^6 H(1, 0, z) + 72 (-1 + y)^4\\&\quad \times (-1 + z)^4 (-1 + y + z) (y + z)^6 (40 y^3 + 24 y^2 (-2 + z) + 3 y (4 - 7 z + 6 z^2) + 3 z (3 - 12 z + 10 z^2))\\&\quad \times H(1, 1, z) - 72 (-1 + y)^4 y (3 + 10 y^2 + 6 y (-2 + z) - 3 z) (-1 + z)^4 (-1 + y + z) (y + z)^6 H(1, 2, y)\\&\quad + 72 (-1 + y)^4 (-1 + z)^4 z (-1 + y + z) (y + z)^6 (3 - 12 z + 10 z^2 + y (-3 + 6 z)) H(2, 0, y) \\&\quad + 288 (-1 + y)^4 (-1 + z)^4 (-1 + y + z) (y + z)^6 (10 y^3 + 6 y^2 (-2 + z) + y (3 - 6 z + 6 z^2)\\&\quad + z (3 - 12 z + 10 z^2)) H(2, 2, y)\Bigg \}\Big /\Big (144 (-1 + y)^4 y (-1 + z)^4 z (-1 + y + z) (y + z)^6\Big );\\ \mathcal {A}_{6;C_{F}n_{f}}^{(2)}&= \Bigg \{45 (-1 + z)^3 z^6 (2 - 2 z + z^2) + 3 y^{11} (15 - 6 z - 39 z^2 + 28 z^3) - 3 y (-1 + z)^2 z^5 (180 - 528 z + 506 z^2 - 167 z^3\\&\quad + 6 z^4) + 3 y^{10} (-75 + 179 z + 81 z^2 - 417 z^3 + 224 z^4) + y^9 (495 - 2538 z + 2541 z^2 + 3020 z^3 - 5974 z^4\\&\quad + 2432 z^5) + y^8 (-585 + 5121 z - 10623 z^2 + 3201 z^3 + 13112 z^4 - 15226 z^5 + 5024 z^6) - 3 y^2 z^4 (450 - 2184 z \end{aligned}$$
$$\begin{aligned}&+ 4776 z^2 - 5694 z^3 + 3541 z^4 - 847 z^5 - 81 z^6 + 39 z^7) + 2 y^7 (180 - 2613 z + 8541 z^2 - 11754 z^3\\&+ 2089 z^4 + 12163 z^5 - 11756 z^6 + 3180 z^7) + y^3 z^3 (-1800 + 13656 z - 34518 z^2 + 41110 z^3\\&- 23508 z^4 + 3201 z^5 + 3020 z^6 - 1251 z^7 + 84 z^8) + 2 y^4 z^2 (-675 + 6828 z - 24831 z^2 \\&+ 39456 z^3 - 26784 z^4 + 2089 z^5 + 6556 z^6 - 2987 z^7 + 336 z^8) + 2 y^5 z (-270 + 3276 z\\&- 17259 z^2 + 39456 z^3 - 38370 z^4 + 7389 z^5 + 12163 z^6 - 7613 z^7 + 1216 z^8) \\&+ 2 y^6 (-45 + 1332 z - 7164 z^2 + 20555 z^3 - 26784 z^4 + 7389 z^5 + 13973 z^6 - 11756 z^7\\&+ 2512 z^8) - 12 (-1 + y)^2 (-1 + 4 y) (-1 + z)^2 (y + z)^6 (-2 + 2 y^3 + 4 z - 3 z^2 + z^3 + y^2 (-6 + 4 z)\\&+ y (6 - 8 z + 3 z^2)) H(1, y) + 3 (-1 + y)^2 (-1 + z)^2 (32 y^{10} + y^9 (-101 + 244 z)\\&+ 3 y^8 (37 - 241 z + 280 z^2) - z^6 (-2 + 4 z - 3 z^2 + z^3) + 2 y^7 (-22 + 351 z - 1125 z^2 + 856 z^3)\\&+ y z^5 (-36 + 4 z + 54 z^2 - 39 z^3 + 4 z^4) + 6 y^2 z^4 (69 - 146 z + 118 z^2 - 55 z^3 + 12 z^4) \\&+ 2 y^3 z^3 (-348 - 98 z + 825 z^2 - 659 z^3 + 200 z^4) + 6 y^5 z (-6 - 206 z + 527 z^2 - 726 z^3 + 332 z^4)\\&+ 2 y^4 z^2 (207 - 198 z + 1263 z^2 - 1518 z^3 + 572 z^4) + 2 y^6 (1 - 98 z + 1110 z^2 - 1987 z^3 + 1132 z^4))\\&\times H(1, z) + 3 (-1 + y)^2 (-1 + z)^2 (32 y^{10} + 5 y^9 (-21 + 52 z) + 3 y^8 (41 - 269 z + 328 z^2) \\&+ 6 y^7 (-10 + 145 z - 469 z^2 + 384 z^3) + z^6 (10 - 60 z + 123 z^2 - 105 z^3 + 32 z^4) \\&+ 6 y^2 z^4 (89 -302 z + 516 z^2 - 469 z^3 + 164 z^4) + y z^5 (12 - 348 z + 870 z^2 - 807 z^3 + 260 z^4) \\&+ 6 y^5 z (2 - 302 z + 927 z^2 - 1400 z^3 + 724 z^4) + 2 y^3 z^3 (-268 - 778 z + 2781 z^2 - 2961 z^3 + 1152 z^4)\\&+ 2 y^4 z^2 (267 - 778 z + 3213 z^2 - 4200 z^3 + 1860 z^4) + 2 y^6 (5 - 174 z + 1548 z^2 - 2961 z^3\\&+ 1860 z^4)) H(2, y)\Bigg \}\Big / \Big (36 (-1 + y)^2 y (-1 + z)^2 z (-1 + y + z) (y + z)^6\Big ). \end{aligned}$$