Parametric Integrals for Binomial Series with Harmonic Polynomials

Abstract

Binomial series involving harmonic polynomials are expressed in terms of parametric integrals. By evaluating these parametric integrals, we establish several remarkable closed formulae for the infinite series containing both central binomial coefficients and harmonic numbers. Most of the values for binomial series found in this paper concern the dilogarithm and trilogarithm functions.