一个Malmstén积分的简单计算
Simple evaluation of one of Malmstén's integrals
摘要：
第4.325.7号从Gradshteyn和Ryzhik的积分表的对数积分首先评价Malmstén。最近，Blagouchine使用轮廓积分方法来评估一个家庭的对数积分，其中包含这个积分。我们主要通过实分析以简单直接的方式计算积分。评价的主要成分是使用等比级数和Kummer的傅里叶级数展开的对数的Γ函数。
英文摘要：
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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