Integral transformations of hypergeometric functions with several variables

TL;DR

This paper introduces a new class of integral transformations for hypergeometric functions with multiple variables, generalizing Riemann-Liouville integrals to broader classes of convergent power series.

Contribution

It presents a novel method for transforming hypergeometric functions of several variables, expanding the analytical tools available for their study.

Findings

New integral transformations for multivariable hypergeometric functions

Generalization of Riemann-Liouville integral to multiple variables

Potential applications in solving complex differential equations

Abstract

As a generalization of Riemann-Liouville integral, we introduce integral transformations of convergent power series which can be applied to hypergeometric functions with several variables.