On the matrix version of new extended Gauss, Appell and Lauricella hypergeometric functions

TL;DR

This paper introduces new matrix extensions of classical hypergeometric functions, including Gauss, Appell, and Lauricella functions, and explores their properties such as integral representations and recurrence relations.

Contribution

It presents novel matrix extensions of hypergeometric functions and analyzes their fundamental properties, expanding the theoretical framework of matrix special functions.

Findings

New matrix extensions of hypergeometric functions introduced

Derived integral representations and differential formulas

Established recurrence relations for the extended functions

Abstract

Inspired by certain interesting recent extensions of the gamma, beta and hypergeometric matrix functions, we introduce here new extension of the gamma and beta matrix function. We also introduce new extensions of the Gauss hypergeometric matrix function, confluent hypergeometric matrix function, Appell matrix function and Lauricella matrix function of three variables in terms of the new extended beta matrix function. Then we investigate certain properties of these extended matrix functions such as the integral representations, differential formulae and recurrence relations.