On generalized Humbert matrix polynomials

Abstract

Aktaş et. al. in [3] introduced the generalized Humbert matrix polynomials (G-HMP) P A n .m; x; y; c/. In this paper we focus on some properties of these matrix polynomials such as matrix recurrence relations, matrix differential equation and an integral representation. We introduce generalized forms of operational rules associated with operators corresponding to a G-HMP expansions. Moreover, we obtain a series transformation formula involving Gegenbauer matrix polynomials. Then we provide a number of applications.