Certain classes of Bilateral Generating Functions involving multiple series with arbitrary terms

Abstract

In this paper we have established three theorems on bilateral generating relations for functions of several variables. In Theorem 1 the bilateral generating relation for two multiple series with essentially arbitrary terms is obtained while the Theorem 2 is its confluent case. The Theorem 3 aims at deriving a new generalization of the confluent form of the Theorem 2.

As applications of these theorems the bilateral generating functions for multivariable hypergeometric polynomials are obtained. Certain expansion formulae involving generalized Lauricella function of several variables are also derived. Some polynomial expansion for hypergeometric series of one and more variables and certain bilateral generating functions for celebrated hypergeometric polynomials are also mentioned as known special cases of our main findings.