Summary

DescriptionSm in the complex plane.svg	English: ${\displaystyle \operatorname {sm} z}$ in the complex plane, illustrating its double periodicity (${\displaystyle \omega =e^{2\pi i/3}}$).[1]
Date	23 April 2022
Source	Own work
Author	A1E6

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1. ↑ Dark areas represent zeros, and bright areas represent poles. As the argument of ${\displaystyle \operatorname {sm} z}$ changes from ${\displaystyle -\pi }$ (excluding ${\displaystyle -\pi }$) to ${\displaystyle \pi }$, the colors go through cyan, blue (${\displaystyle \operatorname {Arg} \approx -\pi /2}$), magneta, red (${\displaystyle \operatorname {Arg} \approx 0}$), orange, yellow (${\displaystyle \operatorname {Arg} \approx \pi /2}$), green, and back to cyan (${\displaystyle \operatorname {Arg} \approx \pi }$).