Reverse generalized Bessel matrix differential equation, polynomial solutions, and their properties

Abstract

This paper is devoted to the study of reverse generalized Bessel matrix polynomials (RGBMPs) within complex analysis. This study is assumed to be a generalization and improvement of the scalar case into the matrix setting. We give a definition of the reverse generalized Bessel matrix polynomials Θn(A; B; z), , for parameter (square) matrices A and B, and provide a second-order matrix differential equations satisfied by these polynomials. Subsequently, a Rodrigues-type formula, a matrix recurrence relationship, and a pseudo-generating function are then developed for RGBMPs. © 2013 The Authors Mathematical Methods in the Applied Sciences Published by John Wiley & Sons, Ltd.