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Computation and theory of extended Mordell-Tornheim-Witten sums

Bailey, David H. and Borwein, Jonathan M. and Crandall, Richard E. (2014) Computation and theory of extended Mordell-Tornheim-Witten sums. Mathematics of Computation (83). pp. 1795-1821.

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    Abstract

    We consider some fundamental generalized Mordell{Tornheim{Witten (MTW)zeta-function values along with their derivatives, and explore connections with multiple-zeta values (MZVs). To achieve this, we make use of symbolic integration, high precisionnumerical integration, and some interesting combinatorics and special-function theory.Our original motivation was to represent unresolved constructs such as Eulerian log-gamma integrals. We are able to resolve all such integrals in terms of a MTW basis. Wealso present, for a substantial subset of MTW values, explicit closed-form expressions. Inthe process, we signi cantly extend methods for high-precision numerical computation ofpolylogarithms and their derivatives with respect to order.

    Item Type: Article
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Mrs Naghmana Tehseen
    Date Deposited: 21 Sep 2016 12:01
    Last Modified: 21 Sep 2016 12:01
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1750

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