SHOGUN  v3.0.0
JacobiEllipticFunctions.h File Reference

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## Classes

class  CJacobiEllipticFunctions
Class that contains methods for computing Jacobi elliptic functions related to complex analysis. These functions are inverse of the elliptic integral of first kind, i.e.

$u(k,m)=\int_{0}^{k}\frac{dt}{\sqrt{(1-t^{2})(1-m^{2}t^{2})}} =\int_{0}^{\varphi}\frac{d\theta}{\sqrt{(1-m^{2}sin^{2}\theta)}}$

where $$k=sin\varphi$$, $$t=sin\theta$$ and parameter $$m, 0\le m \le 1$$ is called modulus. Three main Jacobi elliptic functions are defined as $$sn(u,m)=k=sin\theta$$, $$cn(u,m)=cos\theta=\sqrt{1-sn(u,m)^{2}}$$ and $$dn(u,m)=\sqrt{1-m^{2}sn(u,m)^{2}}$$. For $$k=1$$, i.e. $$\varphi=\frac{\pi}{2}$$, $$u(1,m)=K(m)$$ is known as the complete elliptic integral of first kind. Similarly, $$u(1,m'))= K'(m')$$, $$m'=\sqrt{1-m^{2}}$$ is called the complementary complete elliptic integral of first kind. Jacobi functions are double periodic with quardratic periods $$K$$ and $$K'$$. More...

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