Symmetric Tornheim double zeta functions

Let $s,t,u \in {\mathbb{C}}$ and $T(s,t,u)$ be the Tornheim double zeta function. We investigate some properties of symmetric Tornheim double zeta functions. As a corollary, we give explicit evaluation formulas for $T(s,t,u)$ in terms of series of the gamma function and Riemann zeta function.