Polylogarithmic Connections With Euler Sums

Abstract

Abstract. Polylogarithmic functions are intrinsically connected with sums of harmonic numbers. In this paper we explore many relations and explicitly derive closed form representations of integrals of polylogarithmic functions and the Lerch phi transcendent in terms of zeta functions and sums of alternating harmonic numbers.

Identities in the spirit of Euler

“…The work in this paper also extends the results of [7], [20]. Other works including, [2], [3], [13], [14], [15], [17], and [18] cite many identities of polylogarithmic integrals and Euler sums.…”