逆ディーエヌ関数 arcdn(x,k)

\(\normalsize Inverse\ Jacobi\ elliptic\ function\ arcdn(x,k)\\ (1)\ x=dn(u,k)\hspace{5px}\rightarrow\hspace{5px} u=arcdn(x,k)\equiv dn^{\tiny -1}(x,k)\\ (2)\ arcdn(x,k)=F(\sqrt{1-x^2}/k,k)\ ,\hspace{20px} \sqrt{1-k^2}\le x\le1\\ \hspace{20px}F(x,k)={\large\int_{\small 0}^{\small x}\frac{dt}{\sqrt{(1-t^2)(1-k^2t^2)}}}\ ,\hspace{20px} -1\le x\le1\\ (3)\ k^2sn^2(u,k)+dn^2(u,k)=1\\\)