On partly bilateral and partly unilateral generating functions

Source abstract

Abstract The purpose of this work is to begin the development of a theory of generating functions that will not only include the generating functions which are partly bilateral and partly unilateral but also provide a set of expansions, by taking successive partial derivatives with respect to one of the variables of the generating relations. Our starting point is a result of Exton [4] on associated Laguerre polynomials whose application gives certain generating functions of the polynomials of Jacobi and Appell, and functions of n variables of Lauricella.