A study of generalized hypergeometric Matrix functions via two-parameter Mittag–Leffler matrix function
Jain Shilpi,
Goyal Rahul,
Oros Georgia Irina,
Agarwal Praveen,
Momani Shaher
Affiliations
Jain Shilpi
Department of Mathematics, Poornima College of Engineering, Jaipur, India
Goyal Rahul
Department of Mathematics, Anand International College of Engineering, Jaipur-303012, India
Oros Georgia Irina
Department of Mathematics and Computer Science, Faculty of Informatics and Sciences, University of Oradea, 1 Universitat, ii Str., 410087 Oradea, Romania
Agarwal Praveen
Department of Mathematics, Anand International College of Engineering, Jaipur-303012, India
Momani Shaher
Department of Mathematics, Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman P.O. Box 346, United Arab Emirates
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.
