A symmetry relation for generalized potential polynomials and its applications

Abstract

We prove a general symmetric identity involving the generalized potential polynomials and a polynomial determined by quotient of two formal power series, which unifies several known and new identities for a plenty number of polynomials and numbers defined by exponential generating functions. One of the consequences of this relation yields recently published symmetry relations for Bernoulli polynomials and numbers. Relations are also given for Eulerian, Euler, Genocchi, Apostol-Bernoulli, Apostol-Euler polynomials and their consequences are given. We also generalize the symmetric identity for the degenerate Bernoulli polynomials for a positive integer order.