Accesso libero

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

INFORMAZIONI SU QUESTO ARTICOLO

Cita

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.

ISSN:
1210-3195
Lingua:
Inglese
Frequenza di pubblicazione:
3 volte all'anno
Argomenti della rivista:
Mathematics, General Mathematics