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Review of Computer Engineering Research

March 2015, Volume 2, 1, pp 1-21

Some Relations on Gegenbauer Matrix Polynomials

Ayman Shehata

Ayman Shehata 1

  1. 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 1

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Pages: 1-21

DOI: 10.18488/journal.76/2015.2.1/76.1.1.21

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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. 
Contribution/ Originality
This study is one of very few studies which have been investigated to new families of Gegenbauer matrix polynomials of two variables with two and three matrices is introduced using integral transform method and allow the derivation of a wealth of relations involving these matrix polynomials, and discuss its various special cases and their applications are presented. These results allow us to note that the use of the method of the integral representation is a fairly important tool of analysis and can be usefully extended to other families of Gegenbauer matrix polynomials which is a problem for further work.

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