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jacobiCN

Jacobi elliptic function cn

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Syntax

jacobiCN(u,m)

Description

jacobiCN(u,m) represents the Jacobi elliptic function cn.

Let . Then the Jacobi elliptic function cn is defined as follows:

The Jacobi functions are defined for complex values of u and m.

The Jacobi functions are meromorphic and doubly periodic with periods and with respect to u.

For m = 0 and m = 1, the Jacobi functions reduce to trigonometric or constant functions.

If one argument is a floating-point number, and the other one can be converted to a floating-point number, then a floating-point number is returned.

Environment Interactions

When called with floating-point arguments, these functions are sensitive to the environment variable DIGITS which determines the numerical working precision.

Examples

Example 1

For most arguments, the Jacobi elliptic functions return themselves unevaluated:

jacobiCN(2,1/2)

Floating-point numbers are returned if at least one of the arguments is a floating-point number:

jacobiCN(1.5,1/2)

Floating-point evaluation can be enforced by using float:

float(jacobiCN(1,-1))

Example 2

For m = 0 and m = 1, the result is expressed using a trigonometric function:

jacobiCN(u,0)

jacobiCN(u,1)

Parameters

m

An arithmetical expression specifying the parameter.

Return Values

Arithmetical expression.

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