# 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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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.