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arXiv · 2011.07498

A correlation function for the classical orthogonal polynomials

Enno Diekema
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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.

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Enno Diekema. 2020-11-15. A correlation function for the classical orthogonal polynomials. https://arxiv.org/abs/2011.07498

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