Author(s)

Wathek Chammam^1*, Arjun K. Rathie², Mongia Khlifi³, Muhammad Gulistan⁴

¹Department of Mathematics, College of Science, Majmaah University, Al Majmaah, Saudi Arabia.
²Department of Mathematics, Vedant College of Engineering & Technology (Rajasthan Technical University), Bundi, India.
³Department of Mathematics, Faculty of Sciences of Sfax, Sfax University, Sfax, Tunisia.
⁴Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada.

In this study, we aim to explore a novel class of twenty-five double integrals involving generalized hypergeometric functions. These integrals take the form: $\begin{array}{c}{\displaystyle {\int }_0^1{\displaystyle {\int }_0^1{y}^c}}{\left(1-x\right)}^{c-1}{\left(1-y\right)}^{c-1}{\left(1-xy\right)}^{1-2c}\\ {}_{3}F{}_2\left[\begin{array}{c}a,b,c+\frac{1}{2}\\ \frac{1}{2}\left(a+b+i+1\right),2c+j\end{array};\frac{4y\left(1-x\right)\left(1-y\right)}{{\left(1-xy\right)}^2}\right]\text{d}x\text{d}y\end{array}$ for $i,j=0,\pm 1,\pm 2$ . 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.

Generalized Hypergeometric Function, Watson Theorem, Definite Integral, Beta Integral

Chammam, W. , Rathie, A. , Khlifi, M. and Gulistan, M. (2025) Analysis of a New Class of Double Integrals Involving Generalized Hypergeometric Functions. Journal of Applied Mathematics and Physics, 13, 3831-3841. doi: 10.4236/jamp.2025.1311214.