On the Askey--Wilson type integrals

2019/12/02 by Chuanan Wei, Wei, Chuanan
Mathematics · #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1912.01407

openalex publication_date 2019/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Askey--Wilson integral is very important in the theory of orthogonal polynomials. Liu's integral is a generalization of the Askey--Wilson integral with many parameters. With the help of the series rearrangement method, we give the elementary proof of them. Furthermore, we establish two new Askey--Wilson type integrals in the similar way and find a generalization of a known transformation formula containing three ₃ϕ₂ series.

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