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Integrals of inverse trigonometric and polylogarithmic functions
The Ramanujan Journal ( IF 0.6 ) Pub Date : 2020-09-18 , DOI: 10.1007/s11139-020-00319-1
Anthony Sofo

In this paper we study the representation of integrals whose integrand involves the product of a polylogarithm and an inverse or inverse hyperbolic trigonometric function. We further demonstrate many connections between these integrals and Euler sums. We develop recurrence relations and give some examples of these integrals in terms of Riemann zeta values, Dirichlet values and other special functions.



中文翻译:

逆三角函数和对数函数的积分

在本文中,我们研究积分的表示形式,该积分的被积涉及一个多对数与一个反或反双曲三角函数的乘积。我们进一步证明了这些积分与欧拉和之间的许多联系。我们开发递归关系,并根据黎曼zeta值,狄利克雷值和其他特殊函数给出这些积分的一些示例。

更新日期:2020-09-20
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