SETS OF THE GENERATING FUNCTIONS FOR THE POLYNOMIALS HAVING GENERALIZED APPELL’S REPRESENTATION )) ( ) ( ) ( ( ) ( 2 t F t xG t Hx tA + + ψ

Abstract

This work is motivated by the class of generating functions established earlier by Boas and Buck 
(1956) and later on the extension given by Rainville (1960). In a recent paper (2003), author has found a natural 
extension of the above classes which are capable of yielding new generating functions for a large number of 
new and known polynomial sets. This paper deals with two sets of generating functions obtained for the class 
of polynomial sets which has generalized Appell’s representation of the form )) ( )( ) ( (   ) ( 2 tF t xG tHx tA + + ψ . For 
these sets of generating functions, the recurrence relations and applications have been discussed. Some classes 
of polynomials suggested by Geganbauer,  Hermite and Laguerre polynomials follow as special cases of our 
findings