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Derivative and fast evaluation of the witten Zeta function

Borwein, Jonathan M. and Dilcher, K. (2016) Derivative and fast evaluation of the witten Zeta function. (Submitted)

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Abstract

We study analytic properties of the Witten zeta functionW(r;s;t),which is also named after Mordell and Tornheim. In particular, we evaluate the function W(s;s;�s) (� >0) at s= 0 and, as our main result, nd 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 e�efficient and high-precision evaluations of the Witten zeta function.

Item Type: Article
Subjects: UNSPECIFIED
Faculty: UNSPECIFIED
Depositing User: Mrs Naghmana Tehseen
Date Deposited: 05 Sep 2016 20:27
Last Modified: 05 Sep 2016 20:27
URI: https://docserver.carma.newcastle.edu.au/id/eprint/1741

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