%sn

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();
m=0.36;
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

• delip — полный и неполный эллиптический интеграл первого рода
• %k — Jacobi's complete elliptic integral