Generating functions on extended Jacobi polynomials from Lie group view point

Generating functions play a large role in the study of special functions. The present paper deals with the derivation of some novel generating functions of extended Jacobi polynomials by the application of group-theoretic method introduced by Louis Weisner. In fact, by suitably interpreting the index $(n)$ and the parameter $(\beta)$ of the polynomial under consideration we define four linear partial differential operators and on showing that they generate a Lie-algebra, we obtain a new generating relation (3.3) as the main result of our investigation. Furthermore, some generating functions of Laguerre, Hermite, Bessel and Jacobi polynomials are obtained as the special cases of our main result. Some applications of our results are also pointed out.