A study of generalized hypergeometric Matrix functions via two-parameter Mittag–Leffler matrix function

Abstract

The main aim of this article is to study a new generalizations of the Gauss hypergeometric matrix and confluent hypergeometric matrix functions by using two-parameter Mittag–Leffler matrix function. In particular, we investigate certain important properties of these extended matrix functions such as integral representations, differentiation formulas, beta matrix transform, and Laplace transform. Furthermore, we introduce an extension of the Jacobi matrix orthogonal polynomial by using our generalized Gauss hypergeometric matrix function, which is very important in scattering theory and inverse scattering theory.

Keywords

• matrix functional calculus
• mittag–leffler matrix function
• gamma matrix function
• beta matrix function
• gauss hypergeometric matrix function
• confluent hypergeometric matrix function
• beta matrix transform and laplace transform