Integrals of powers of loggamma

Amdeberhan, Tewodros; Coffey, Mark; Espinosa, Olivier; Koutschan, Christoph; Manna, Dante; Moll, Victor

doi:10.1090/S0002-9939-2010-10589-0

Integrals of powers of loggamma
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by Tewodros Amdeberhan, Mark W. Coffey, Olivier Espinosa, Christoph Koutschan, Dante V. Manna and Victor H. Moll PDF

Proc. Amer. Math. Soc. 139 (2011), 535-545 Request permission

Abstract:

Properties of the integral of powers of $\log \Gamma (x)$ from $0$ to $1$ are considered. Analytic evaluations for the first two powers are presented. Empirical evidence for the cubic case is discussed.

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