Some properties of -gamma, -beta and -hypergeometric matrix functions

In this paper, we investigate the matrix analogues of the psi-beta and psi-gamma functions, as well as their properties. With the help of the psi-beta matrix function (BMF), we introduce the psi-Gauss hypergeometric matrix function (GHMF) and the psi-Kummer hypergeometric matrix function (KHMF) and derive certain properties for these matrix functions. Finally, the psi-Appell and the psi-Lauricella matrix functions are defined by applications of the psi-BMF, and their integral representations are also given.