`jacobiAM`

Jacobi amplitude function.

Category: Mathematics > Mathematical Functions

Syntax

Y = jacobiAM(u, m)

Evaluates the function at u for the parameter m.

Description

jacobiAM returns the angle phi for which ellipticF(phi, m) = u. 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];
jacobiAM(u, 0.3)
ellipticF(jacobiAM(0.5, 0.3), 0.3)

Output

ans = 1×3

    0.1996    0.4941    0.9593
ans = 0.5000

jacobiAM