Polylogarithmic Connections With Euler Sums
DOI:
https://doi.org/10.5644/SJM.12.1.02Keywords:
Polylogarithm function, integral representation, Lerch transcendent function, alternating harmonic numbers, combinatorial series identities, summation formulas, partial fraction approach, binomial coefficientsAbstract
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.
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