arXiv 1701.044842017-01-16math.NT

Power series with skew-harmonic numbers, dilogarithms, and double integrals

Khristo N. Boyadzhiev

备注：: 15 pages
发表信息：: Tatra Mountains Mathematical Publications, 56(2013) 93-108

英文摘要：

The skew-harmonic numbers are the partial sums of the alternating harmonic series, i.e. the expansion of log(2). 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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