# Jacobi elliptic function sn,cn,dn (chart) Calculator

## Calculates a table of the Jacobi elliptic function sn(u,k), cn(u,k) and dn(u,k) and draws the chart.

 k -1≦k≦1 [ initial value u increment repetition ]
 $\normal Jacobi\ elliptic\ functions\\\hspace{120} sn(u,k),\ cn(u,k),\ dn(u,k)\\[10](1)\ sn(u,k)=sin(am(u,k))\\[10](2)\ am(u,k)=\phi=F^{-1}(u,k)\\\hspace{25}u=F(\phi,k)={\large\int_{\small 0}^{\hspace{25pt}\phi}\frac{d\theta}{\sqrt{1-k^2sin^2\theta}}}\\[10](3)\ cn(u,k)=\sqrt{1-sn^2(u,k)}\\\hspace{25}dn(u,k)=\sqrt{1-k^2sn^2(u,k)}\\[10](4)\ sn^2(u,k)+cn^2(u,k)=1\\\hspace{25}k^2sn^2(u,k)+dn^2(u,k)=1\\$

Jacobi elliptic function sn,cn,dn (chart)
 [1-6] /6 Disp-Num5103050100200
[1]  2017/04/28 00:03   - / 50 years old level / A teacher / A researcher / Very /
Purpose of use
See what the solution of an ODE from quantum theory looks like
Comment/Request
The period of sn does not seem to be very accurate for m = 0.999999
[2]  2014/12/23 23:07   Male / 60 years old level or over / A teacher / A researcher / Very /
Comment/Request
I should appreciate it very much if it is extended to sc, nc, and dc (imaginary argument).
[3]  2014/04/15 03:16   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Investigating properties of the Jacobi elliptic functions.
[4]  2013/06/06 08:33   Male / 20 years old level / Others / Very /
Purpose of use
MONOGRAFIAS
[5]  2013/02/27 06:44   Male / 30 years old level / A teacher / A researcher / Very /
Purpose of use
Wanted to see the behavior of the functions in a plot.
[6]  2011/08/28 08:17   Male / 60 years old level / Others / Very /
Purpose of use
Comment/Request
Excellent !

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