Investigation for the pRq-hypergeometric matrix functions and associated properties

Abstract

We investigate the matrix analogues of the ${}_{p}R_{q}$-beta and ${}_{p}R_{q}$-gamma functions, as well as their properties, in this paper. We introduce the ${}_{p}R_{q}$-Gauss hypergeometric matrix function (GHMF) and the ${}_{p}R_{q}$-Kummer hypergeometric matrix function (KHMF) and derive certain properties for these matrix functions using the ${}_{p}R_{q}$-beta matrix function. Finally, the ${}_{p}R_{q}$-Appell and ${}_{p}R_{q}$-Lauricella matrix functions are defined through applications of the ${}_{p}R_{q}$-BMF, and their integral representations are provided.