论文标题
对数 - 三角学积分和椭圆函数
Log-trigonometric integrals and elliptic functions
论文作者
论文摘要
根据椭圆函数评估了一类对数基因组合的积分。通过此，通过使用椭圆形积分值，可以获得诸如\ [\ int \ limits_0^{π/{2}}} \ ln \ left（\ cosh \ frac {x} {x} {x} {X} {\ sqrt {\ sqrt {3}}+cos \ frac \ frac \ ln { x \ right）}} {\ sqrt {3}} \ right）dx = \ frac {π^2} {8 \ sqrt {3}} - \fracπ{4} \ ln \ ln \ left（1+\ sqrt \ sqrt {3} {3} \ right）
A class of log-trigonometric integrals are evaluated in terms of elliptic functions. From this, by using the elliptic integral singular values, one can obtain closed form evaluations of integrals such as \[ \int\limits_0^{π/{2}}\ln\left(\cosh\frac{x}{\sqrt{3}}+\cos\frac{\ln \left(2\cos x\right)}{\sqrt{3}}\right)dx=\frac{π^2}{8\sqrt{3}}-\fracπ{4}\ln\left(1+\sqrt{3}\right)+\frac{13π}{24}\ln 2. \]
