Power series with skew-harmonic numbers, dilogarithms, and double integrals
Number Theory
2017-01-18 v1
Abstract
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.
Cite
@article{arxiv.1701.04484,
title = {Power series with skew-harmonic numbers, dilogarithms, and double integrals},
author = {Khristo N. Boyadzhiev},
journal= {arXiv preprint arXiv:1701.04484},
year = {2017}
}
Comments
15 pages