`jacobiND`

Jacobi elliptic function nd(u|m) = 1/dn(u|m).

Category: Mathematics > Mathematical Functions

Syntax

Y = jacobiND(u, m)

Returns nd(u|m), the reciprocal of dn(u|m).

Description

dn(u|m) is the third basic Jacobi function, sqrt(1 - m*sn(u|m)^2). nd is its reciprocal. At u = 0 the value is exactly 1.

For m = 0 the function is identically 1.

Input arguments

u: Argument, a numeric or symbolic value or array.
m: Parameter of the elliptic function, m = k^2, where k is the modulus. Scalar or an array compatible with u.

Output arguments

Y: Values of the function, with the size of the inputs.

Example

Evaluate at a point and over a vector

jacobiND(0.5, 0.3)
jacobiND([0 0.5 1], 0.3)

Output

ans = 1.0355
ans = 1×3

    1.0000    1.0355    1.1188

Notes

The parameter m is the square of the modulus, not the modulus itself. For m = 0 the Jacobi functions reduce to ordinary trigonometric functions, and for m = 1 to hyperbolic ones.

jacobiND