English

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 2φ1_2\varphi_1-Bessel function on a qq-quadratic grid. Dick Askey suggested that the ``Bessel-type orthogonality'' at the 2φ1_2\varphi_1-level has really a general character and can be extended up to the 8φ7_8\varphi_7-level. Very-well-poised 8φ7_8\varphi_7-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 8φ7_8\varphi_7-functions. Another type of the orthogonality relation for a very-well-poised 8φ7_8\varphi_7-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}
}
R2 v1 2026-07-22T17:56:53.321Z