Journal of Integer Sequences, Vol. 25 (2022), Article 22.5.5

Tornheim-Like Series, Harmonic Numbers, and Zeta Values

Ilham A. Aliev and Ayhan Dil
Department of Mathematics
Akdeniz University
07070 Antalya


We obtain explicit evaluations of the Tornheim-like multiple series involving harmonic numbers. We give a new relationship between harmonic numbers and ζ(2). We also present closed-form formulas of some multiple series in terms of zeta values.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A000110 A001008 A263633.)

Received December 6 2021; revised versions received December 9 2021; April 5 2022; April 6 2022. Published in Journal of Integer Sequences, June 20 2022.

Return to Journal of Integer Sequences home page