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: Ramanujan Journal Vol. 36, Issue 1, p. 43-68
Publisher Link: http://dx.doi.org/10.1007/s11139-012-9427-1
Publisher: Springer
Resource Type: journal article
Date: 2015
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 [formula could not be replicated] 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 funtion; Riemann zeta function; Tornheim-Weitten zeta function; integration
Identifier: http://hdl.handle.net/1959.13/1314534
Identifier: uon:22779
Identifier: ISSN:1382-4090
Language: eng
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