Srivastava-Pintér theorems for 2D-Appell polynomials and their applications

Abstract

Recently, Srivastava and Pinter proved addition theorems for the generalized Bernoulli and Euler polynomials. Luo and Srivastava obtained the anologous results for the generalized Apostol–Bernoulli polynomials and the generalized Apostol–Euler polynomials. Finally, Tremblay et al. gave analogues of the Srivastava–Pinter addition theorem for general family of Bernoulli polynomials. In this paper, we obtain Srivastava–Pinter type theorems for 2D-Appell Polynomials. We also give the representation of 2D-Appell Polynomials in terms of the Stirling numbers of the second kind and 1D-Appell polynomials. Furthermore, we introduce the unified 2D-Apostol polynomials. In particular, we obtain some relations between that family of polynomials and the generalized Hurwitz–Lerch zeta function as well as the Gauss hypergeometric function. Finally, we present some applications of Srivastava–Pinter type theorems for 2D-Appell Polynomials. Copyright © 2013 John Wiley & Sons, Ltd.