- 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 LGn = ∫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
- Reviewed
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