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

Author:

Jain Shilpi1,Goyal Rahul2,Oros Georgia Irina3,Agarwal Praveen245,Momani Shaher46

Affiliation:

1. Department of Mathematics, Poornima College of Engineering , Jaipur , India

2. Department of Mathematics, Anand International College of Engineering , Jaipur-303012 , India

3. Department of Mathematics and Computer Science, Faculty of Informatics and Sciences, University of Oradea, 1 Universitat, ii Str. , 410087 Oradea , Romania

4. Department of Mathematics, Nonlinear Dynamics Research Center (NDRC), Ajman University , Ajman P.O. Box 346 , United Arab Emirates

5. Department of Mathematics, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St , 117198 Moscow , Russian Federation

6. Department of Mathematics, Faculty of Science, University of Jordan , Amman 11942 , Jordan

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

General Physics and Astronomy

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