Certain Relations of Gegenbauer and Modified Gegenbauer Matrix Polynomials by Lie Algebraic Method

Abstract

The object of the present paper is to derive the generating formulae for the Gegenbauer and modified Gegenbauer matrix polynomials by introducing a partial differential operatorand constructing the Lie algebra representation formalism of special linear algebra by using Weisner’s group-theoretic approach. Application of our results is also pointed out.

Keywords

• gegenbauer matrix polynomials
• generating matrix functions
• matrix differential equations
• differential operator
• group-theoretic method