jacobiCD

Jacobi elliptic function cd(u, m) = cn/dn.

Category: Mathematics > Mathematical Functions

Syntax

Y = jacobiCD(u, m)

Description

jacobiCD returns the quotient cn(u,m)/dn(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];
jacobiCD(u, 0.3)
jacobiCD(0.5, 0)

ans = 1×3

    0.9860    0.9117    0.6423
ans = 0.8776

See also

jacobiCN jacobiSN jacobiDN ellipticF ellipticK