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arXiv · 1709.08435

Simple evaluation of one of Malmstén's integrals

Uwe Bäsel
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Abstract

The logarithmic integral no. 4.325.7 from Gradshteyn and Ryzhik's tables of integrals was first evaluated by Malmstén. Recently, Blagouchine used contour integration methods to evaluate a family of logarithmic integrals that contains this integral. We evaluate the integral in a simple, straightforward manner mainly by means of real analysis. The main ingredients of the evaluation are the use of geometric series and Kummer's Fourier series expansion for the logarithm of the gamma function.

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Uwe Bäsel. 2017-09-25. Simple evaluation of one of Malmstén's integrals. https://arxiv.org/abs/1709.08435

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