# 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} }

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…

## 14 Citations

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The numerical computation of derivatives at zero of a specialization originating in a preprint by Romik and the experimental evaluation of these numerical values in terms of well-known constants is described.

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Log-sine-polylog integrals and alternating Euler sums

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The log-sine-polylog integrals were introduced by J. M. Borwein and A. Straub during their studies on special values of the log-sine integrals. In this paper we evaluate some of the log-sine-polylog…

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