The role of Jacobi polynomials in the theory of Hermite and Laguerre 2D polynomials

DOI10.1016/S0377-0427(02)00632-5zbMath1015.33005MaRDI QIDQ1874188

Yanyan Li

Publication date: 22 May 2003

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

unimodular transformationsaddition theorem for Jacobi polynomialsrepresentations of linear groups

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Cites Work

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• Operational rules and arbitrary order Hermite generating functions
• Arbitrary-order Hermite generating functions for obtaining arbitrary-order coherent and squeezed states
• Generating functions for Hermite polynomials of arbitrary order
• Laguerre 2D-functions and their application in quantum optics
• Transformations of Laguerre 2D polynomials with applications to quasiprobabilities
• General Hermite and Laguerre two-dimensional polynomials
• Asymptotic formulae for two-variable Hermite polynomials
• Hermite and Laguerre \(2D\) polynomials

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