Decomposition formulas associated with the multivariable confluent hypergeometric functions

TL;DR

This paper develops new decomposition formulas for multivariable confluent hypergeometric functions using elementary operator techniques, simplifying these complex functions into products of simpler Gauss hypergeometric functions.

Contribution

It introduces a novel approach employing inverse pairs of symbolic operators to derive decomposition formulas for multivariable confluent hypergeometric functions.

Findings

Derived several decomposition formulas for multivariable confluent hypergeometric functions.

Expressed complex hypergeometric functions as products of simpler Gauss hypergeometric functions.

Established operator identities that facilitate these decompositions.

Abstract

The main object of this work is to show how some rather elementary techniques based upon certain inverse pairs of symbolic operators would lead us easily to several decomposition formulas associated with confluent hypergeometric functions of two and more variables. Many operator identities involving these pairs of symbolic operators are first constructed for this purpose. By means of these operator identities several decomposition formulas are found, which express the aforementioned hypergeometric functions in terms of such simpler functions as the products of the Gauss hypergeometric functions.