On the Askey-Wilson polynomials and a q-beta integral

Zhi Guo Liu

doi:10.1090/proc/15584

On the Askey-Wilson polynomials and a q-beta integral

Zhi Guo Liu^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

A proof of the orthogonality relation for the Askey-Wilson polynomials is given by using a generating function for the Askey-Wilson polynomials and the uniqueness of a rational function expansion. We further use the orthogonality relation for the Askey-Wilson polynomials and a q-series transformation formula to evaluate a general q-beta integral with eight parameters. The integrand of this q-beta integral is the product of two terminating 5φ4 series and the value is a 10φ₉ series.

Original language	English
Pages (from-to)	4639-4648
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	149
Issue number	11
DOIs	https://doi.org/10.1090/proc/15584
State	Published - Nov 2021

Keywords

Askey-Wilson integral
Askey-Wilson polynomials
Double q-series
Q-beta integral

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AB - A proof of the orthogonality relation for the Askey-Wilson polynomials is given by using a generating function for the Askey-Wilson polynomials and the uniqueness of a rational function expansion. We further use the orthogonality relation for the Askey-Wilson polynomials and a q-series transformation formula to evaluate a general q-beta integral with eight parameters. The integrand of this q-beta integral is the product of two terminating 5φ4 series and the value is a 10φ9 series.

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KW - Double q-series

KW - Q-beta integral

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ER -

On the Askey-Wilson polynomials and a q-beta integral

Abstract

Keywords

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