# Jacobian Elliptic Function (G Dataflow)

Version:
Last Modified: January 9, 2017

Determines the Jacobian elliptic function.  ## x

The input argument.

Default: 0 ## k

The integrand parameter. ## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: No error ## cn

Value of the Jacobi elliptic function cn. ## dn

The Jacobi elliptic function dn. ## sn

Value of the Jacobi elliptic function sn. ## phi

The upper limit of the integral defining the function. ## error out

Error information. The node produces this output according to standard error behavior.

## Algorithm for Calculating the Jacobian Elliptic Function

The following equations define the Jacobian elliptic function.

$cn\left(x,k\right)=\mathrm{cos}\left(\varphi \right)$
$\mathrm{sn}\left(x,k\right)=\mathrm{sin}\left(\varphi \right)$
$\mathrm{dn}\left(x,k\right)=\sqrt{1-k{\mathrm{sin}}^{2}\varphi }$

where

$x={\int }_{0}^{\varphi }\frac{1}{\sqrt{1-k{\mathrm{sin}}^{2}\theta }}d\theta$

The function is defined according to the following intervals for the input values.

$x\in \Re ,k\in \left[0,1\right]$

For any real value of integrand parameter k in the unit interval, the function is defined for all real values of x.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported