On General Alternating Tornheim-Type Double Series

In this paper, we express ${\sum }_{n,m\ge 1}\frac{{\epsilon }_1^n{\epsilon }_2^m{M}_n^{\left(u\right)}{M}_m^{\left(v\right)}}{n^r{m}^s{(n+m)}^t}$ as a linear combination of alternating multiple zeta values, where ${\epsilon }_i\in \{1,-1\}$ and $M_k^{\left(u\right)}\in \{H_k^{\left(u\right)},{\overline{H}}_k^{\left(u\right)}\}$, with $H_k^{\left(u\right)}$ and ${\overline{H}}_k^{\left(u\right)}$ 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.