Identities on Generalized Apostol-Genocchi Numbers and Polynomials Involving Binomial Coefficients

Abstract

In [11], Jolany et al. defined generalizations of Apostol-Genocchi numbers and polynomials. Most identities on classical or generalized Apostol-Genocchi numbers and polynomials are related to the well-known Bernoulli and Euler numbers and polynomials. However, in this paper, identities on generalized Apostol-Genocchi numbers and polynomials which are not associated with the Bernoulli- and Euler-types are introduced. Specifically, identities involving binomial coefficients and some integral identities which only relate generalized Apostol-Genocchi numbers and polynomials are established.