Generalized Mittag-Leffler Matrix Function and Associated Matrix Polynomials

The Mittag-Leffler function has been found useful in solving certain problems in Science and Engineering. On the other hand, noticing the occurrence of certain matrix functions in Special functions’ theory in general and in Statistics and Lie group theory in particular, we introduce here a matrix analogue of a recently generalized form of Mittag-Leffler function. This function yields the matrix analogues of the Saxena-Nishimoto’s function, Bessel-Maitland function, Dotsenko function and the Elliptic Function. We obtain matrix differential equation and eigen matrix function property for the proposed matrix function. Also, a generalized Konhauser matrix polynomial is deduced and its inverse series relations and generating function are derived.