MATLAB Function Reference Volume 1: A - E - Bad Request

2ellipj
Purpose Jacobi elliptic functions
Syntax [SN,CN,DN] = ellipj(U,M)
[SN,CN,DN] = ellipj(U,M,tol)
Definition The Jacobi elliptic functions are defined in terms of the integral:
u
Then
=
∫
dθ
1 msin θ 2
φ
------------------------------------ 1
0
--
( – ) 2
sn( u)
= sinφ, cn( u)
= cosφ,
dn( u)
1 msin φ 2
= ( – ) 2,
am( u)
= φ
Some definitions of the elliptic functions use the modulus k instead of the
parameter m . They are related by
k2 m sin α 2
= =
The Jacobi elliptic functions obey many mathematical identities; for a good
sample, see [1].
Description [SN,CN,DN] = ellipj(U,M) returns the Jacobi elliptic functions SN, CN, and
DN, evaluated for corresponding elements of argument U and parameter M.
Inputs U and M must be the same size (or either can be scalar).
[SN,CN,DN] = ellipj(U,M,tol) computes the Jacobi elliptic functions to
accuracy tol. The default is eps; increase this for a less accurate but more
quickly computed answer.
Algorithm ellipj computes the Jacobi elliptic functions using the method of the
arithmetic-geometric mean [1]. It starts with the triplet of numbers:
1
1
--
--
2
2
a0 = 1, b0 = ( 1 – m)
, c0 =
( m)
1
--
ellipj
2-481