楕円関数 sn,cn,dn（グラフ）

\(\normalsize Jacobi\ elliptic\ functions\\ \hspace{120px} sn(u,k),\ cn(u,k),\ dn(u,k)\\ (1)\ sn(u,k)= \sin(am(u,k))\\ (2)\ am(u,k)=\phi=F^{-1}(u,k)\\ \hspace{25px}u=F(\phi,k)={\large\int_{\small 0}^{\phi}\frac{d\theta}{\sqrt{1-k^2 \sin^2\theta}}}\\ (3)\ cn(u,k)=\sqrt{1-sn^2(u,k)}\\ \hspace{25px}dn(u,k)=\sqrt{1-k^2sn^2(u,k)}\\ (4)\ sn^2(u,k)+cn^2(u,k)=1\\ \hspace{25px}k^2sn^2(u,k)+dn^2(u,k)=1\\\)