TITLE:
Analysis of a New Class of Double Integrals Involving Generalized Hypergeometric Functions
AUTHORS:
Wathek Chammam, Arjun K. Rathie, Mongia Khlifi, Muhammad Gulistan
KEYWORDS:
Generalized Hypergeometric Function, Watson Theorem, Definite Integral, Beta Integral
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.11,
November
13,
2025
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.