On Eulerian log-gamma integrals and Tornheim–Witten zeta functions

@article{Bailey2015OnEL,
title={On Eulerian log-gamma integrals and Tornheim–Witten zeta functions},
author={David H. Bailey and David Borwein and Jonathan Michael Borwein},
journal={The Ramanujan Journal},
year={2015},
volume={36},
pages={43-68}
}
• Published 1 February 2015
• Mathematics
• The Ramanujan Journal
AbstractStimulated by earlier work by Moll and his coworkers (Amdeberhan et al., Proc. Am. Math. Soc., 139(2):535–545, 2010), 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 $$\mathcal{LG}_n=\int_0^1 \log^n\varGamma(x) \,\mathrm{d}x$$ for 1≤n≤4 and make some comments regarding the general case. The subsidiary computational challenges…
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