一个定积分的计算
Computation of a Definite Integral
摘要:
作为柯西定理的一个应用,我们证明了$\int_0^1\arctan\left({\arctanh x-\arctan x\over π+\arctanh x-\arctan x}\right) {dx\over x}= {π\over 8}\log{π^2\over 8}$回答了一个问题,首先张贴在数学堆栈交换,然后在MathOverflow。
英文摘要:
As an application of Cauchy's Theorem we prove that $\int_0^1\arctan\left({\arctanh x-\arctan x\over π+\arctanh x-\arctan x}\right) {dx\over x}= {π\over 8}\log{π^2\over 8}$ answering a question first posted in Mathematics Stack Exchange and then in MathOverflow.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。