SOME RELATIONS ON THE GENERALIZED BESSEL MATRIX POLYNOMIALS
AYMAN SHEHATA *
Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt. and Department of Mathematics, College of Science and Arts, Unaizah, Qassim University, Qassim, Kingdom of Saudi Arabia.
*Author to whom correspondence should be addressed.
The main aim of this paper is to develop the generalized Bessel matrix polynomials. We derive the various families of the generating matrix functions for the generalized hypergeometric matrix function. Some new, known and unknown generating matrix functions involving the generalized Bessel matrix polynomials are obtained by using the hypergeometric matrix function as applications of the main results. We give connections between generalized Bessel and Jacobi matrix polynomials. An expansion formula of these matrix polynomials is given. We get some generating matrix functions for the generalized Bessel matrix polynomials, involving the Horn’s and hypergeometric matrix functions. The results obtained here include a number of linear, bilinear and bilateral generating matrix functions for the generalized Bessel matrix polynomials which further leads to certain recent generalizations of the known and unknown bilinear and bilateral generating matrix functions and give some applications of the obtained results.
Keywords: Bessel matrix polynomials, Hypergeometric matrix functions, Linear, bilinear and bilateral generating matrix functions