%sn

Scilab Function
Last update : 12/01/2004

%sn - Jacobi 's elliptic function

### Calling Sequence

  `[y]=%sn(x,m)`

### Parameters

- `x` : a point inside the fundamental rectangle defined by the elliptic integral; `x` is a vector of complex numbers
- `m` : parameter of the elliptic integral (`0<m<1` )
- `y` : result

### Description

Jacobi 's sn elliptic function with parameter `m` : the inverse of the elliptic integral for the parameter `m` .

The amplitude am is computed in fortran and the addition formulas for elliptic functions are applied

### Examples

    m=0.36;
    K=%k(m);
    P=4*K; //Real period
    real_val=0:(P/50):P;
    plot(real_val,real(%sn(real_val,m)))
    xbasc();
    KK=%k(1-m);
    Ip=2*KK;
    ima_val1=0:(Ip/50):KK-0.001;
    ima_val2=(KK+0.05):(Ip/25):(Ip+KK);
    z1=%sn(%i*ima_val1,m);z2=%sn(%i*ima_val2,m);
    plot2d([ima_val1',ima_val2'],[imag(z1)',imag(z2)']);
    xgrid(3)

### See Also

`%asn` , `%k` ,

### Author

F. D.