振幅関数 am(u,k)（グラフ）

\(\normalsize Jacobi\ amplitude\ am(u,k)\\ (1)\ am(u,k)=\phi=F^{-1}(u,k),\hspace{20px} |am(u,k)|\le \pi\\ \hspace{25px}u=F(\phi,k)={\large\int_{\small 0}^{\phi}\frac{d\theta}{\sqrt{1-k^2 \sin^2\theta}}}\\ (2)\ sn(u,k)= \sin(am(u,k)) = \sin\phi\\ \hspace{25px}cn(u,k)= \cos(am(u,k))= \cos\phi\\ \hspace{25px}dn(u,k)=\frac{\partial am(u,k)}{\partial u} \\\)