The multiplication formulas for the Apostol-Genocchi polynomials

Abstract

We obtain the multiplication formulas for the ApostolGenocchi polynomials of higher order by using the generalized multinomial identity. We introduce the λ-multiple alternating sums and show some explicit recursive formulas of the Apostol-Genocchi polynomials of higher order. Apostol-Bernoulli numbers and polynomials of higher order, Apostol-Genocchi numbers and polynomials of higher order, multinomial identity, multiplication formula, λ-multiple alternating sums.