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was defined by the first-named author (see [5, 8]). It can be meromorphically continued to the whole space Cr+1, and possible singularities of (1.1) can be explicitly determined (see [8, Theorem 1]). In the 1950’s, Tornheim considered the double series ζMT,2(p, q; r) (p, q, r ∈ N), and gave some fascinating formulas (see [16]). A little later, Mordell independently studied the values ζMT,2(k, k; k) (k ∈ N), and showed that ζMT,2(2p, 2p; 2p) can be written as Mp · π6p for some constant Mp ∈ Q (p ∈ N) (see [11]). About 30 years later, Subbarao and Sitaramachandrarao gave an evaluation formula for ζMT,2(2p, 2p; 2p) ([14]). Then Zagier [22] proved the following simple formula:

On value-relations, functional relations and singularities of Mordell–Tornheim and related triple zeta-functions