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

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