论文标题
对数积分：Gradshteyn和Ryzhik到最近的评论
Logarithmic Integrals: A Review from Gradshteyn and Ryzhik to Recent Times
论文作者
论文摘要
在基本上所有定量领域，包括数学科学，物理科学的基本上，评估对数积分的需求无处不在。物理学的一些最新发展，即Feynman图表涉及涉及对数功能的复杂积分的评估。这项工作介绍了从Malmsten积分开始到I. S. S. Gradshteyn和I. M. Ryzhik [1]再到最近时代的对数积分开始的对数积分的系统综述。对这些类型积分的评估涉及较高的先验功能（即Hurwitz Zeta函数，Polyrogarithms，Lerch先验，正交多项式，Polygamma函数）。从更一般的意义上讲，这项工作考虑了以下类型的积分：\ begin {align*} \ int_ {0}^{a} f（x）\ ln {\ {g（x）\}} \ dx \ dx \ dx \ end {align*}，in r^{+} $，$ f（x）$和$ g（x）$和$ g（x）$都是ratighation/trigon/trigonometric或两种型号的函数。
The need to evaluate Logarithmic integrals is ubiquitous in essentially all quantitative areas including mathematical sciences, physical sciences. Some recent developments in Physics namely Feynman diagrams deals with the evaluation of complicated integrals involving logarithmic functions. This work deals with a systematic review of logarithmic integrals starting from Malmsten integrals to classical collection of Integrals, Series and Products by I. S. Gradshteyn and I. M. Ryzhik [1] to recent times. The evaluation of these types of integrals involves higher transcendental functions (i.e., Hurwitz Zeta function, Polylogarithms, Lerch Transcendental, Orthogonal Polynomials, PolyGamma functions). In a more general sense the following types of integrals are considered for this work: \begin{align*} \int_{0}^{a} f(x) \ln{\{g(x)\}} \ dx \end{align*} with $a \in R^{+}$ , $f(x)$ and $g(x)$ both either rational/trigonometric or both type of functions.
