Derivatives and Fast Evaluation of the Witten Zeta Function
نویسندگان
چکیده
We study analytic properties of the Witten zeta function W(r, s, t), which is also named after Mordell and Tornheim. In particular, we evaluate the function W(s, s, τs) (τ > 0) at s = 0 and, as our main result, find the derivative of this function at s = 0. Our principal tool is an identity due to Crandall that involves a free parameter and provides an analytic continuation. Furthermore, we derive special values of a permutation sum. Throughout this paper we show by way of examples that Crandall’s identity can be used for efficient and high-precision evaluations of the Witten zeta function.
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