**Subuhi Khan, Ghazala Yasmin, Archana Mittal**

## On
Generating Relations Involving Generalized Gegenbauer Polynomials

**Abstract:**

In this paper, generating relations involving generalized Gegenbauer polynomials
$C_n^{(\mu)}(x,y;\alpha)$ are obtained by constructing a three-dimensional Lie
algebra isomorphic to special linear algebra sl(2). Further, a number of new
interesting relations involving various generalized polynomials are obtained as
applications of these generating relations.

**Keywords:**

Generalized Gegenbauer polynomials, Lie group, Lie algebra, generating
relations.

**MSC 2000:** 33C50, 33C80, 33C05