シーディー関数 cd(u,k)

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