<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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 trilogarithm which are related to our results. Finally, we provide the evaluations of several double integrals in terms of classical constants.</p></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 trilogarithm which are related to our results. Finally, we provide the evaluations of several double integrals in terms of classical constants.

POWER SERIES WITH SKEW-HARMONIC NUMBERS, DILOGARITHMS, AND DOUBLE INTEGRALS

Tatra Mountains Mathematical Publications

{"article-title":"POWER SERIES WITH SKEW-HARMONIC NUMBERS, DILOGARITHMS, AND DOUBLE INTEGRALS"}

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...

POWER SERIES WITH SKEW-HARMONIC NUMBERS, DILOGARITHMS, AND DOUBLE INTEGRALS

Published Online: Feb 18, 2014

Page range: 93 - 108

DOI: https://doi.org/10.2478/tmmp-2013-0031

This content is open access.