`jacobiCN`

Jacobi elliptic function cn(u, m).

Category: Mathematics > Mathematical Functions

Syntax

Y = jacobiCN(u, m)

Evaluates the function at u for the parameter m.

Description

jacobiCN returns the cosine of the amplitude, cos(am(u, m)). The Jacobi functions generalize the circular functions: they are doubly periodic and arise as inverses of the incomplete elliptic integral of the first kind, ellipticF. When m = 0 they reduce to ordinary trigonometric functions of u, and when m approaches 1 to hyperbolic ones.

Input arguments

u: Argument, numeric or symbolic; may be an array.
m: Parameter (m = k^2), with 0 <= m <= 1 for real behavior.

Output arguments

Y: Array formed by broadcasting u and m.

Example

Values and the circular limit

u = [0.2 0.5 1];
jacobiCN(u, 0.3)
jacobiCN(0.5, [0 0.3 0.9])

Output

ans = 1×3

    0.9801    0.8804    0.5741
ans = 1×3

    0.8776    0.8804    0.8859

jacobiCN