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

Abstract

Inspired by certain interesting recent extension 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 new extended  matrix functions such as the integral  representations, differential formulae and recurrence relations.