On a representation of Humbert's double hypergeometric series in a series of Gauss's 2F1 function

TL;DR

This paper derives a new representation of Humbert's double hypergeometric series using Gauss's 2F1 function, providing new insights and special cases.

Contribution

It introduces a novel series representation of Humbert's hypergeometric function in terms of Gauss's 2F1, expanding the analytical tools for hypergeometric functions.

Findings

Representation of Humbert's hypergeometric function in terms of 2F1.

Special cases derived from the main representation.

New identities and relations for hypergeometric functions.

Abstract

In this paper, we aim to obtain a representation of Humbert's hy- pergeometric function in a series of Gauss's function 2F1. A few interesting results have also been deduced as special case of our main findings.