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

Nestor Gonzales Acala, Edward Rowe Aleluya

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.

Keywords

Apostol number, Genocchi number, Apostol polynomial, Genocchi polynomial, Binomial coefficients, Binomial inversion formula

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