Generating Relations of the Hypergeometric Functions by the Lie Group-Theoretic Method

In this paper, the generating relations for a set of hypergeometric functions _,,,m (x) are obtained by using the representation of the Lie group SL(2,C) giving a suitable interpretation to the index m in order to derive the elements of Lie algebra. The principle interest in our results lies in the fact that a number of special cases would inevitably yield too many new and known results of the theory of special functions, namely the Laguerre, even and odd generalized Hermite, Meixner, Gottlieb, and Krawtchouk polynomials.