Fourier series representations of the logarithms of the Euler gamma function and the Barnes multiple gamma functions

Details Fourier series representations of the logarithms of the Euler gamma function and the Barnes multiple gamma functions Fourier series representations of the logarithms of the Euler gamma function and the Barnes multiple gamma functions

2009-03-25

arxiv.org/abs/0903.4323v1

Mathematics

Classical Analysis and ODEs

Scientific paper

Kummer's Fourier series for the log gamma function is well known, having been
discovered in 1847. In this paper we develop a corresponding Fourier series for
the logarithm of the Barnes double gamma function (and the method may be easily
extended to higher order multiple gamma functions). Some applications of these
Fourier series are explored.

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