A $(p,\nu)$-extension of Srivastava's triple hypergeometric function and its properties

TL;DR

This paper introduces a new $(p, u)$-extended version of Srivastava's triple hypergeometric function using an extended Beta function, and explores its key properties including integral representations, transforms, and inequalities.

Contribution

It presents a novel $(p, u)$-extension of Srivastava's triple hypergeometric function and derives its fundamental properties, expanding the theoretical framework of hypergeometric functions.

Findings

Derived integral representations involving Exton's hypergeometric function

Established Mellin transform and differential formulas

Proved bounded inequalities for the extended function

Abstract

In this paper, we obtain a $(p,\nu)$-extension of Srivastava's triple hypergeometric function $H_B(\cdot)$, together by using the extended Beta function $B_{p,\nu}(x,y)$ introduced in arXiv:1502.06200. We give some of the main properties of this extended function, which include several integral representations involving Exton's hypergeometric function, the Mellin transform, a differential formula, recursion formulas and a bounded inequality.