Some new formulas for the products of the Apostol type polynomials

Abstract

In the year 2014, Kim et al. computed a kind of new sums of the products of an arbitrary number of the classical Bernoulli and Euler polynomials by using the Euler basis for the vector space of polynomials of bounded degree. Inspired by their work, in this paper, we establish some new formulas for such a kind of sums of the products of an arbitrary number of the Apostol-Bernoulli, Euler, and Genocchi polynomials by making use of the generating function methods and summation transform techniques. The results derived here are generalizations of the corresponding known formulas involving the classical Bernoulli, Euler, and Genocchi polynomials.