Work

Analysis of a New Class of Double Integrals Involving Generalized Hypergeometric Functions

Year: 2025

Type: article

Abstract: In this study, we aim to explore a novel class of twenty-five double integrals involving generalized hypergeometric functions. These integrals take the form: ∫ 0 1 ∫ 0 1 y c ( 1−x ) c−1 ( 1−y ) c−1 ( 1−xy ) 1−2c F 3 2 [ a,b,c+ 1 2 1 2 ( a+b+i+1 ),2c+j ; 4y( 1−x )( 1−y ) ( 1−xy ) 2 ]dxdy for i,j=0,±1,±2 . The results are derived using generalized versions of Watson’s summation theorem, as established in earlier work by Lavoie et al. Additionally, fifty integrals, split into two sets of twenty-five, are presented as special cases of our main findings, offering further insights into the structure of these integrals.

Source: Journal of Applied Mathematics and Physics

DOI: 10.4236/jamp.2025.1311214

Authors: Wathek Chammam, Arjun K. Rathie, Mongia Khlifi, Muhammad Gulistan

Institutions: Majmaah University, Rajasthan Technical University, University of Sfax, Faculty of Sciences of Sfax, University of Alberta

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Majmaah University

Award: G8234167073