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… 
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14 Citations
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Methods Citations
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14 Citations

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TLDR
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Log-sine-polylog integrals and alternating Euler sums
  • I. Mezo
  • Mathematics
    Acta Mathematica Hungarica
  • 2019
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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References

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This work considers some fundamental generalized Mordell{Tornheim{Witten} zeta-function values along with their derivatives, and explores connections with multiple- zeta values (MZVs), and signicantly extend methods for high-precision numerical computation of polylogarithms and their derivatives with respect to order.
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