A correlation function for the classical orthogonal polynomials
Classical Analysis and ODEs
2020-11-17 v1
Abstract
A correlation function of the classical orthogonal polynomials is defined and determined. The correlation function obeys a second order difference equation in two variables. The correlation function for the Gegenbauer, Chebyshev and Legendre polynomials can be written as a 4F3 hypergeometric function. For the Jacobi polynomials the result is an F2 Appell function. For the Generalized Laguerre polynomials the result is a confluent hypergeometric function and for the Hermite polynomials there rests only a single term.
Cite
@article{arxiv.2011.07498,
title = {A correlation function for the classical orthogonal polynomials},
author = {Enno Diekema},
journal= {arXiv preprint arXiv:2011.07498},
year = {2020}
}