求解 y=sinpi/x

$$y = \sin \frac { \pi } { x }$$

求解 x 的值 (复数求解)

$$\left\{\begin{matrix}\\x=\frac{\pi i}{\ln(-\sqrt{1-y^{2}}+iy)+2i\pi n_{2}}\text{, }n_{2}\in \mathrm{Z}\text{, }&\text{unconditionally}\\x=\frac{\pi i}{\ln(\sqrt{1-y^{2}}+iy)+2i\pi n_{1}}\text{, }n_{1}\in \mathrm{Z}\text{, }n_{1}\neq \frac{i\ln(\sqrt{1-y^{2}}+iy)}{2\pi }\text{, }&y\neq 0\end{matrix}\right.$$

求解 y 的值

$$y=\sin(\frac{\pi }{x})$$

$$x\neq 0$$