Generalizations of generating functions for basic hypergeometric orthogonal polynomials
Classical Analysis and ODEs
2018-06-01 v4
Abstract
We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one free parameter to them. In particular, we generalize generating functions for the Askey-Wilson, continuous -ultraspherical/Rogers, little -Laguerre/Wall, and -Laguerre polynomials. Depending on what type of orthogonality these polynomials satisfy, we derive corresponding definite integrals, infinite series, bilateral infinite series, and -integrals.
Cite
@article{arxiv.1411.1371,
title = {Generalizations of generating functions for basic hypergeometric orthogonal polynomials},
author = {Howard S. Cohl and Roberto S. Costas-Santos and Philbert R. Hwang and Tanay Wakhare},
journal= {arXiv preprint arXiv:1411.1371},
year = {2018}
}