ellipj

Jacobi elliptic functions sn, cn and dn.

Category: Mathematics > Elementary Math

Syntax

[sn, cn, dn] = ellipj(u, m)

Description

The Jacobi functions generalize sine and cosine. With m = 0 they reduce to sin(u), cos(u) and 1; with m = 1 they become tanh(u), sech(u) and sech(u). They satisfy sn^2 + cn^2 = 1 and dn^2 = 1 - m*sn^2. They are used for the exact motion of a pendulum and in elliptic filter design.

Input arguments

u

Real argument (array).

m

Parameter, with 0 <= m <= 1. Note that m is the square of the modulus k.

Output arguments

sn, cn, dn

Values of sn(u|m), cn(u|m) and dn(u|m).

Example

Jacobi functions for m = 0.3

[sn, cn, dn] = ellipj(0.5, 0.3)
sn^2 + cn^2

sn = 0.4742
cn = 0.8804
dn = 0.9657
ans = 1

See also

ellipke sin cos tanh