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%sn

Jacobi's elliptic function

Syntax

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
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

History

VersionDescription
6.1.0 %sn() is declared obsolete. ellipj() must be used instead.
6.1.1 %sn() will be removed from the next Scilab version

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