その他関数

\[\mathrm{rect}\left(x\right)=H_{\frac{1}{2}}\left(x+\frac{1}{2}\right)-H_{\frac{1}{2}}\left(x-\frac{1}{2}\right)\]

\[\mathrm{tri}\left(x\right)=\mathrm{rect}\left(x\right)*_{x}\mathrm{rect}\left(x\right)\]

\[f\left(x\right):=x\]

\[f\left(x\right):=\begin{cases}-1 & x<0\\0 & x=0\\1 & 0<x\end{cases}\]

\[\mathrm{rect}\left(x\right):=\begin{cases}1 & \left|x\right|<\frac{1}{2}\\\frac{1}{2} & \left|x\right|=\frac{1}{2}\\0 & \frac{1}{2}<\left|x\right|\end{cases}\]

\[\mathrm{tri}\left(x\right):=\max\left(1-\left|x\right|,0\right)\]

\[\tan x+\cos^{-1}x=\sum_{k=0}^{\infty}\frac{\hat{T}_{k}}{k!}x^{k}\]

\[\min\left(-x,x\right)=-\left|x\right|\]

\[\int_{0}^{\infty}sinc^{n}(x)dx=\frac{\pi}{2^{n+1}(n-1)!}\sum_{k=0}^{n}C(n,k)(-1)^{k}(n-2k)^{n-1}\sgn(n-2k)\]

\[\left(\log x\right)^{(-n)}=\left(\log x-H_{n}\right)\frac{x^{n}}{n!}\]