Since the Clausen functions are intimately related to a number of other important special functions, such as Inverse Tangent Integrals, Polylogarithms, Polygamma Functions, Zeta Functions, and more besides - many of which are at the forefront of mode…
\[\Large\sum_{k=1}^{\infty}\frac{(2^{2k-1}-2)(4^{2k+1}-3^{2k+1})}{144^k\,k\,(2k+1)}\zeta(2k)\] \(\Large\mathbf{Solution:}\) Within the interval \(\displaystyle 0\ < x < \pi/2\,\), the logtangent function has the series representation \[\ln(\tan x)=\…
要做成页面只传入数据,js生成图表,如下图 下面是js代码 var LineChart = function (ID, title, axisData,seriesData) { var myChart = echarts.init(document.getElementById(ID)); var newData = []; var legendData = []; for (var i = 0; i < seriesData.length; i++) { var lineItem = new…
Evaluate integral $$\int_{0}^{1}{x^{-x}(1-x)^{x-1}\sin{\pi x}dx}$$ Well,I think we have $$\int_{0}^{1}{x^{-x}(1-x)^{x-1}\sin{\pi x}dx}=\frac{\pi}{e}$$ and $$\int_{0}^{1}{x^{x}(1-x)^{1-x}\sin{\pi x}dx}=\frac{e\pi}{24}$$ With such nice result of…
