Decompositions for hypergeometric function $H_A, H_B,H_C$

TL;DR

This paper develops new decomposition formulas for Srivastava's hypergeometric functions of three variables using inverse pairs of symbolic operators, resulting in 15 decompositions involving products of Gauss and Appell functions.

Contribution

It introduces novel operator identities and decompositions for hypergeometric functions of three variables, expanding the analytical tools available for these functions.

Findings

15 new decompositions derived

Operator identities constructed for hypergeometric functions

Decompositions expressed through products of Gauss and Appell functions

Abstract

With the help of some techniques based on certain inverse pairs of symbolic operators, the authors investigated several decomposition formulas associated with Srivastava's Hypergeometric functions of three variables. Some operator identities have been constructed in this matter. With the help these operator forms 15 decompositions are found which are expressed through product of Hypergeometric Gauss and Appell's functions.