%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.