Some Relations on Gegenbauer Matrix Polynomials

Ayman  Shehata

doi:10.18488/journal.76/2015.2.1/76.1.1.21

Authors

Ayman Shehata Department of Mathematics, Faculty of Science, Assiut University, Egypt; Department of Mathematics, College of Science and Arts in Unaizah, Qassim University,Qassim, Kingdom of Saudi Arabia

DOI:

https://doi.org/10.18488/journal.76/2015.2.1/76.1.1.21

Abstract

The main aim of this paper is devoted to derive some relations of Gegenbauer matrix polynomials of two variables. Volterra integral equation and a new representation of these matrix polynomials are given here. We introduce new generalized various forms of Gegenbauer matrix polynomials of two and three matrices by using the method of integral transforms to Hermite matrix polynomials. Furthermore, families of generating matrix functions are obtained and their applications are presented.

Keywords:

Gegenbauer and hermite matrix polynomials, Matrix differential equations, Volterra integral equation, Integral representations, Generating matrix functions