A class of bilateral generating functions for certain classical polynomials

Abstract

In this paper the authors first prove a theorem on bilateral generating 1 relations for a certain sequence of functions. It is then shown how the main result can be applied to derive a large variety of bilateral generating functions for the Bessel, Jacobi, Her mite, Laguerre and ultraspherical polynomials, as well as for their various generalizations. Some recent results given by W. A. Al-Salam [1], S. K. Chatterjea [2], M. K. Das [3], S. Saran [6] and the present authors [9] are thus observed to follow fairly easily as special cases of the theorem proved in this paper.