New proofs of theorems on q -orthogonal functions

Dandan Chen; Zhiguo Liu

doi:10.1142/S179304212550023X

New proofs of theorems on q -orthogonal functions

Dandan Chen^*
, Zhiguo Liu

^*Corresponding author for this work

School of Mathematical Sciences

Shanghai University

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

Abstract

In this paper, we establish a q-integral formula by using the orthogonality relation, and also provide a new proof of the q-orthogonality relation for the continuous q-ultraspherical polynomials. A new q-beta integral with five parameters is evaluated.

Original language	English
Pages (from-to)	473-486
Number of pages	14
Journal	International Journal of Number Theory
Volume	21
Issue number	2
DOIs	https://doi.org/10.1142/S179304212550023X
State	Published - 1 Mar 2025

Keywords

Askey-Wilson polynomials
q -beta integral
q -orthogonal functions
q -ultraspherical polynomials

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title = "New proofs of theorems on q -orthogonal functions",

abstract = "In this paper, we establish a q-integral formula by using the orthogonality relation, and also provide a new proof of the q-orthogonality relation for the continuous q-ultraspherical polynomials. A new q-beta integral with five parameters is evaluated.",

keywords = "Askey-Wilson polynomials, q -beta integral, q -orthogonal functions, q -ultraspherical polynomials",

author = "Dandan Chen and Zhiguo Liu",

note = "Publisher Copyright: {\textcopyright} 2025 World Scientific Publishing Company.",

year = "2025",

month = mar,

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doi = "10.1142/S179304212550023X",

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T1 - New proofs of theorems on q -orthogonal functions

AU - Chen, Dandan

AU - Liu, Zhiguo

PY - 2025/3/1

Y1 - 2025/3/1

N2 - In this paper, we establish a q-integral formula by using the orthogonality relation, and also provide a new proof of the q-orthogonality relation for the continuous q-ultraspherical polynomials. A new q-beta integral with five parameters is evaluated.

AB - In this paper, we establish a q-integral formula by using the orthogonality relation, and also provide a new proof of the q-orthogonality relation for the continuous q-ultraspherical polynomials. A new q-beta integral with five parameters is evaluated.

KW - Askey-Wilson polynomials

KW - q -beta integral

KW - q -orthogonal functions

KW - q -ultraspherical polynomials

UR - https://www.scopus.com/pages/publications/85209380156

U2 - 10.1142/S179304212550023X

DO - 10.1142/S179304212550023X

M3 - 文章

AN - SCOPUS:85209380156

SN - 1793-0421

VL - 21

SP - 473

EP - 486

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 2

ER -

New proofs of theorems on q -orthogonal functions

Abstract

Keywords

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