jacobiDS

Jacobi elliptic function ds(u, m) = dn/sn.

Category: Mathematics > Mathematical Functions

Syntax

Y = jacobiDS(u, m)

Description

jacobiDS returns the quotient dn(u,m)/sn(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];
jacobiDS(u, 0.3)
jacobiDS(0.5, 0)

ans = 1×3

    5.0135    2.0364    1.0916
ans = 2.0858

See also

jacobiCS jacobiSN jacobiDN ellipticF ellipticK