`jacobiSD`

Jacobi elliptic function sd(u|m) = sn(u|m)/dn(u|m).

Category: Mathematics > Mathematical Functions

Syntax

Y = jacobiSD(u, m)

Returns sd(u|m), the quotient of sn by dn.

Description

sd(u|m) = sn(u|m)/dn(u|m). Because dn never vanishes for real u and 0 <= m < 1, sd is finite for all real arguments there. For m = 0 it equals sin(u).

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

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

Output

ans = 0.4911
ans = 1×3

         0    0.4911    0.9161

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.

jacobiSD