New proofs of theorems on <i>q</i>-orthogonal functions

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.

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Publication Details

Journal
International Journal of Number Theory
Published
2024-09-30
DOI
https://doi.org/10.1142/s179304212550023x
Primary Topic
Advanced Optimization Algorithms Research
Type
article
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article

New proofs of theorems on q-orthogonal functions

Dandan Chen, Zhiguo Liu
International Journal of Number Theory
Advanced Optimization Algorithms Research
article

New proofs of theorems on q-orthogonal functions

Dandan Chen, Zhiguo Liu
article en

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.

International Journal of Number TheoryVol. 21(02)
Shanghai University (CN), East China Normal University (CN)
Openalex Percentile: Top 74%
Advanced Optimization Algorithms Research
DOISourceOpenAlex
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New proofs of theorems on <i>q</i>-orthogonal functions — Dandan Chen, Zhiguo Liu · International Journal of Number Theory (2024) | TGRS Research Map | TGRS