Generating functions via integral transforms

In this paper, we use some integral transforms to derive, for a polynomial sequence {Pn(x)} n 0, generating functions of the type Gγ (x, t) = ∞ n=0 γnPn(x)tn, starting from a generating function of type G(x, t) = ∞ n=0 Pn(x)tn, where {γn} n 0 is a real numbers sequence independent on x and t . That allows us to unify the treatment of a generating function problem for many well-known polynomial sequences in the literature. © 2006 Elsevier Inc. All rights reserved