`jacobiSN`

Jacobi elliptic function sn(u|m).

Category: Mathematics > Mathematical Functions

Syntax

Y = jacobiSN(u, m)

Returns sn(u|m), the Jacobi sine amplitude function.

Description

sn(u|m) is defined as sin(phi), where phi is the amplitude of u: the angle for which the incomplete elliptic integral of the first kind F(phi|m) equals u. It is the inverse-function counterpart of that integral and behaves like a sine whose period is stretched to 4*K(m).

Together with the companion functions cn and dn it is also returned by ellipj. The other Jacobi functions in this family are quotients of sn, cn and dn.

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

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

Output

ans = 0.4742
ans = 1×3

         0    0.4742    0.8188

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.

jacobiSN