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 serieswith skew-harmonic numbers. This provides a simultaneous solution of two recent problems byOvidiu Furdui in the American Mathematical Monthly and the College Mathematics Journal. Wealso present and discuss representations involving the dilogarithm and the trilogaithm which arerelated to our results. Finally, we provide the evaluations of several double integrals in terms ofclassical constants.
@article{262,
title = {Power series with skew-harmonic numbers, dilogrithms, and double integrals},
journal = {Tatra Mountains Mathematical Publications},
volume = {58},
year = {2014},
doi = {10.2478/tatra.v56i0.262},
language = {EN},
url = {http://dml.mathdoc.fr/item/262}
}
Boyadzhiev, Khristo N. Power series with skew-harmonic numbers, dilogrithms, and double integrals. Tatra Mountains Mathematical Publications, Tome 58 (2014) . doi : 10.2478/tatra.v56i0.262. http://gdmltest.u-ga.fr/item/262/