On certain Kampé de Fériet-like hypergeometric matrix functions

Abstract

In this paper, we introduce certain Kampé de Fériet-like matrix functions and investigate their regions of convergence and recurrence relations satisfied by them. The importance of studying these matrix functions stems from the fact that the derivatives of arbitrary integral order of confluent hypergeometric matrix function and Gauss hypergeometric matrix function with respect to their matrix parameters can be expressed in the form of these Kampé de Fériet-like matrix functions. Integral representations of these matrix functions in a special case are also given.