On the incomplete hypergeometric matrix functions

By means of the familiar incomplete gamma matrix functions (gamma (A,x)) and (Gamma (A,x)), we introduce the incomplete Pochhammer matrix symbols that lead us to a generalization and decomposition of the incomplete hypergeometric matrix functions (IHMFs). Some properties such as a matrix differential equation, integral expressions and recurrence relations of IHMFs are given. Besides, connections between these matrix functions and other special matrix functions are investigated.