jacobiDN

Jacobi elliptic function dn(u, m).

Category: Mathematics > Mathematical Functions

Syntax

Y = jacobiDN(u, m)

Description

jacobiDN returns sqrt(1 - m*sin(am(u, m))^2). 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];
jacobiDN(u, 0.3)
jacobiDN(0.5, 0)

ans = 1×3

    0.9941    0.9657    0.8938
ans = 1

See also

jacobiCN jacobiSN ellipticF ellipticK