%sn

Jacobi ‘s elliptic function

Calling Sequence

[y]=%sn(x,m)

Arguments

: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)))
`clf`_();
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 elliptic integral
• %k Jacobi’s complete elliptic integral