A class of bilateral generating functions for certain classical polynomials

On a sequence of functions Vn (α,β,δ) (x;a, k, s)

“…where m is non negative integer, the coefficient A m,n are arbitrary constant and f, g, h are suitable functions of x and t. Equation (3.1) is well-known in the literature as the Singhal-Srivastava generating function [7]. Theorem 3.1 (Singhal-Srivastava Theorem [12,7]).…”

Some Generating Functions for the Generalized Bessel Polynomials

“…A very specialized version of Theorem 2 when q = 1 was given recently by Chongdar [10, p. 50, Theorem 6] who seems to have overlooked the fact that his main results [10, p. 46, Theorem 1; p. 47, Theorem 2] are merely disguised forms of the theorem proved, almost two decades ago, by Singhal and Srivastava [26]. Pain [21], on the other hand, gave a group-theoretic derivation of another very specialized version of Theorem 2 when q = 1, a = 0, and 13 = 2.…”

A Class of Generating Functions for the Jacobi and Related Polynomials

“…[5,Chapter 16] and [12,Chapter 4]). With a view to obtaining bilinear, bilateral, or mixed multilateral generating functions for the modified Jacobi polynomials Pn(a-n,fJ-nl(x), several workers (see, for example, [1], [2], [3], [6], [8], and [9] Corollary 5]. The object of the present note is to develop a substantially more general class of mixed generating functions for the Jacobi polynomials as yet another interesting consequence of (1.2).…”