On General Alternating Tornheim-Type Double Series

Abstract

In this paper, we express ∑n,m≥1ε1nε2mMn(u)Mm(v)nrms(n+m)t as a linear combination of alternating multiple zeta values, where εi∈{1,−1} and Mk(u)∈{Hk(u),H¯k(u)}, with Hk(u) and H¯k(u) being harmonic and alternating harmonic numbers, respectively. These sums include Subbarao and Sitaramachandrarao’s alternating analogues of Tornheim’s double series as a special case. Our method is based on employing two different techniques to evaluate the specific integral associated with a 3-poset Hasse diagram.

Keywords

• alternating multiple zeta values
• generalized alternating harmonic numbers
• Mordell–Tornheim series
• alternating Tornheim-type double series
• 3-poset integral