On a new class of Laplace-type integrals involving generalized hypergeometric functions (Q2306617)

Summary: In the theory of generalized hypergeometric functions, classical summation theorems for the series \(_2 F_1\), \(_3 F_2\), \(_4 F_3\), \(_5 F_4\) and \(_7 F_6\) play a key role. Very recently, Masjed-Jamei and Koepf established generalizations of the above-mentioned summation theorems. Inspired by their work, the main objective of the paper is to provide a new class of Laplace-type integrals involving generalized hypergeometric functions \(_p F_p\) for \(p = 2, 3, 4, 5\) and 7 in the most general forms. Several new and known cases have also been obtained as special cases of our main findings.