On a representation of Humbert's double hypergeometric series ${\Phi }_3$ in a series of Gauss's ${}_2{F}_1$ function

Abstract

Very recently a new series representation of Humbert's double hypergeometric series ${\Phi }_3$ in series of Gauss's ${}_2{F}_1$ function was given by one of us. The aim of this short research note is to provide an alternative proof of the result. A few interesting special cases are also given.

6 pages