Some formulae for products of geometric polynomials with applications

Abstract

In this paper, wee evaluate sums and integrals of products of two geometric polynomials and obtain new explicit formulas for geometric polynomials and numbers. As a consequence of these results, we give new explicit formulas for p-Bernoulli numbers, Apostol-Bernoulli functions, and integrals of products of two Apostol-Bernoulli functions.