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On Eulerian Log-Gamma Integrals and Tornheim--Witten zeta functions.

Bailey, David H. and Borwein, David and Borwein, Jonathan M. (2013) On Eulerian Log-Gamma Integrals and Tornheim--Witten zeta functions. Ramanujan J. .

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    Abstract

    Stimulated by earlier work by Moll and his coworkers [1], we evaluate various basic log Gamma integrals in terms of partial derivatives of Tornheim– Witten zeta functions and their extensions arising from evaluations of Fourier series. In particular, we fully evaluate $LGn =\int_o^1\log^n Γ(x) dx$ for $1 ≤ n ≤ 4$ and make some comments regarding the general case. The subsidiary computational challenges are substantial, interesting and significant in their own right.

    Item Type: Article
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Dr David Allingham
    Date Deposited: 05 Oct 2012 13:13
    Last Modified: 28 Nov 2014 15:53
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1377

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