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^*

^*此作品的通讯作者

数学科学学院

科研成果: 期刊稿件 › 文章 › 同行评审

4 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	4639-4648
页数	10
期刊	Proceedings of the American Mathematical Society
卷	149
期	11
DOI	https://doi.org/10.1090/proc/15584
出版状态	已出版 - 11月 2021

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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 - Q-beta integral

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

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