Generating Functions of Chebyshev Polynomials in Three Variables
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In this paper, we obtain generating functions of three-variable Chebyshev polynomials (of the first as well as of the second type) associated with the root system of the A3 Lie algebra. Bibliography: 21 titles.
KeywordsOrthogonal Polynomial Weyl Group Simple Root Chebyshev Polynomial Fundamental Weight
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- 7.B. N. Ryland and H. Z. Munthe-Kaas, “On multivariate Chebyshev polynomials and spectral approximations on triangles. Spectral and high order methods for partial differential equations,” Lect. Notes Comput. Sci. Eng., 76, Berlin, Springer, 19–41 (2011).Google Scholar
- 8.B. Shapiro and M. Shapiro, “On eigenvalues of rectangular matrices,” Trudy MIAN, 267, 258–265 (2009).Google Scholar
- 10.P. P. Kulish, V. D. Lyakhovsky, and O. V. Postnova, “Tensor power decomposition. B n -case,” J. of Physics: Conference Series, 343, 012095 (2012).Google Scholar
- 11.P. P. Kulish, V. D. Lyakhovsky, and O. V. Postnova, “Tensor powers for non-simply laced Lie algebras. B 2 -case,” J. of Physics: Conference Series, 346, 012012 (2012).Google Scholar
- 15.G. Von Gehlen and S. Roan, “The superintegrable chiral Potts quantum chain and generalized Chebyshev polynomials,” in: S. Pakuliak and G. Von Gehlen (eds), Integrable sturctures of exactly solvable two-dimensional models of quantum field theory (Kiev, 2000), NATO Sci. Ser. II, Math. Phys. Chem., 35, Kluwer (2001), pp. 155–172.Google Scholar
- 17.P. K. Suetin, Classical Orthogonal Polynomials [in Russian], Nauka, Moscow (1979).Google Scholar
- 18.N. Bourbaki, 1975 Elements de Mathematique. Groupes et Algebres de Lie Hermann, Paris (1975).Google Scholar
- 19.B. Ken Dunn and R. Lidl, “Generalizations of the classical Chebyshev polynomials to polynomials in two variables,” Czech. Math. J., 32, 516–528 (1982).Google Scholar
- 20.E. V. Damaskinsky, P. P. Kulish, and M. A. Sokolov, “On calculation of generating functions of multivariate Chebyshev polynomials,” POMI preprint 13/2014.Google Scholar
- 21.JiaChang Sun, “A new class of three-variable orthogonal polynomials and their recurrences relations,” Science in China, Series A: Mathematics, 51, 1071–1092 (2008).Google Scholar