A Theoretical Approach on Generating Functions for Some Polynomials and Special Functions by using Lie Laplace Transformation

The process of obtaining generating functions takes place by many methods. Lie group and integral transform are considered of the recent methods for obtaining such kind of generating relations. The aim of this study is to obtain generating functions for some polynomials and special functions by using Lie group theoretic approach and Laplace transform. Most of these generating relations are considered as generalizations of previous results that have been obtained before. This study comprises some new generating functions for some polynomials such as Laguerre, Legendre, Hermite, Jacobi, Gegenbauer and Bessel polynomials. Also generating functions for some special functions of three variables such as Exton’s functions have been established. The main methods used in our work for obtaining the generating relations are Lie group theoretic method and Laplace transform.