Some orthogonal very-well-poised $_8\varphi_7$-functions that generalize Askey-Wilson polynomials
Classical Analysis and ODEs
2016-09-07 v1
Abstract
In a recent paper Ismail, Masson, and Suslov have established a continuous orthogonality relation and some other properties of a -Bessel function on a -quadratic grid. Dick Askey suggested that the ``Bessel-type orthogonality'' at the -level has really a general character and can be extended up to the -level. Very-well-poised -functions are known as a nonterminating version of the classical Askey--Wilson polynomials. Askey's congecture has been proved by the author. In the present paper we discuss in details some properties of the orthogonal -functions. Another type of the orthogonality relation for a very-well-poised -function was recently found by Askey, Rahman, and Suslov.
Keywords
Cite
@article{arxiv.math/9707213,
title = {Some orthogonal very-well-poised $_8\varphi_7$-functions that generalize Askey-Wilson polynomials},
author = {Sergei K. Suslov},
journal= {arXiv preprint arXiv:math/9707213},
year = {2016}
}