Symmetric Tornheim double zeta functions

Abstract

Let $$s,t,u \\in {{\\mathbb {C}}}$$\n and T(s,\xa0t,\xa0u) be the Tornheim double zeta function. In this paper, we investigate some properties of symmetric Tornheim double zeta functions which can be regarded as a desingularization of the Tornheim double zeta function. As a corollary, we give explicit evaluation formulas or rapidly convergent series representations for T(s,\xa0t,\xa0u) in terms of series of the gamma function and the Riemann zeta function.