Power series with skew-harmonic numbers, dilogrithms, and double integrals
Abstract
The skew-harmonic numbers are the partial sums of the alternating harmonic series,
i.e. the expansion of log2. We evaluate in closed form various power series and numerical series
with skew-harmonic numbers. This provides a simultaneous solution of two recent problems by
Ovidiu Furdui in the American Mathematical Monthly and the College Mathematics Journal. We
also present and discuss representations involving the dilogarithm and the trilogaithm which are
related to our results. Finally, we provide the evaluations of several double integrals in terms of
classical constants.
i.e. the expansion of log2. We evaluate in closed form various power series and numerical series
with skew-harmonic numbers. This provides a simultaneous solution of two recent problems by
Ovidiu Furdui in the American Mathematical Monthly and the College Mathematics Journal. We
also present and discuss representations involving the dilogarithm and the trilogaithm which are
related to our results. Finally, we provide the evaluations of several double integrals in terms of
classical constants.
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PDFDOI: https://doi.org/10.2478/tatra.v56i0.262