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

Title: On Eulerian log-gamma integrals and Tornheim–Witten zeta functions
Creator: Bailey, David H.; Borwein, David; Borwein, Jonathan M.
Relation: Ramadujan Journal
Publisher Link: http://dx.doi.org/10.1007/s11139-012-9427-1
Publisher: Springer
Resource Type: journal article
Date: 2013
Description: Stimulated 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 LG_n = ∫₀¹logⁿΓ(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
Subject: gamma function; log-gamma function; Riemann zeta function; Tornheim–Weitten zeta function; integration
Identifier: http://hdl.handle.net/1959.13/940016
Identifier: uon:12922
Identifier: ISSN:1382-4090
Language: eng
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