Correction: On the reflection, diffraction and refraction of a spherical wave of parallel polarization by a sphere of electrically long radius

Correction to: Eur. Phys. J. Plus (2020) 135:240

https://doi.org/10.1140/epjp/s13360-020-00117-0

Editorial corrections and a corrective remark regarding the calculation:

Editorial corrections:

In formula (5.18), last line, inside the radical it should be k₂r, instead of k₂b.

In formula (5.91), in the first term on the right-hand side, the last index of Φ should be +, not ±.

In the legend of Fig. 19, the integration should be Ι_2,3, not l_2,3 (uppercase I, instead of lowercase L).

In the middle of p.99 instead of “as shown is the Fig. 25”, it should be read “as shown in Fig. 25”.

Corrective remark regarding the calculation:

Referring to the discussion ensuing from formula (6.20) and formula (6.21), the following corrective remark applies:

The shift of the contour of integration to argt = π/4 necessitates the inclusion of a separate term corresponding to the residue series contribution from λ = k₁. Integral J_2,1 equals then the result of the calculation of the right-hand side of Eq. (6.16), with the contour of integration along the direction argt = π/4, plus S_p(2),0,+,1.

Likewise, the suggested ways of executing the integration of I_2,1 when all η₂, ξ_b, ξ_r ≪ 1 must avoid the point λ = k₁. Consequently, a deformation of the initial contour of integration (along the real axis) is necessary and therefore, in this case too, S_p(2),0,+,1 should be accounted for separately.

For the above reasons and referring to the first paragraph of Sect. 6, it is recognized that the computation of S_p(2),0,+,1 needs to be considered if the convergence of the residue series from λ = k₁ is slow not only when −η₂ ≫ 1 in the context of formula (5.84), but also when ξ_b, ξ_r ≪ 1 and |η₂|≤ O(1) in the context of the discussion for the calculation of J_2,1 (formula (6.16)).