Combinatorial identities for Appell polynomials

Abstract

Using the techniques of the modern umbral calculus, we derive several combinatorial identities involving s-Appell polynomials. In particular, we obtain identities for classical polynomials, such as the Hermite, Laguerre, Bernoulli, Euler, N?rlund, hypergeometric Bernoulli, and Legendre polynomials. Moreover, we obtain a generalization of Carlitz's identity for Bernoulli numbers and polynomials to arbitrary symmetric s-Appell polynomials.