# Jacobi amplitude function am(u,k) (chart)

## Calculates a table of the Jacobi amplitude function am(u,k) and draws the chart.

k
 -1≦k≦1
[ initial value u
increment
 repetition ]

u am(u,k)

 $\normal Jacobi\ amplitude\ am(u,k)\\[10](1)\ am(u,k)=\phi=F^{-1}(u,k),\hspace{20} |am(u,k)|\le \pi\\\hspace{25}u=F(\phi,k)={\large\int_{\small 0}^{\hspace{25}\phi}\frac{d\theta}{\sqrt{1-k^2sin^2\theta}}}\\[10](2)\ sn(u,k)=sin(am(u,k))=sin\phi\\\hspace{25}cn(u,k)=cos(am(u,k))=cos\phi\\\hspace{25}dn(u,k)=\frac{\partial am(u,k)}{\partial u} \\$

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