Connection Problem for Sums of Finite Products of Legendre and Laguerre Polynomials

The purpose of this paper is to represent sums of finite products of Legendre and Laguerre polynomials in terms of several orthogonal polynomials. Indeed, by explicit computations we express each of them as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer and Jacobi polynom...

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Bibliographic Details
Published in:Symmetry (Basel) 2019-03, Vol.11 (3), p.317
Main Authors: Kim, Taekyun, Hwang, Kyung-Won, Kim, Dae, Dolgy, Dmitry
Format: Article
Language:English
Subjects:
Gegenbauer polynomials
generalized Laguerre polynomials
Hypergeometric functions
hypergeometric functions 1F1 and 2F1
Laguerre polynomials
Legendre polynomials
Polynomials
Quantum field theory
Sums
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Summary:The purpose of this paper is to represent sums of finite products of Legendre and Laguerre polynomials in terms of several orthogonal polynomials. Indeed, by explicit computations we express each of them as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer and Jacobi polynomials, some of which involve terminating hypergeometric functions 1 F 1 and 2 F 1 .
ISSN:2073-8994
2073-8994
DOI:10.3390/sym11030317