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Jacobi elliptic function cn

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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.


Example 1

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


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


Floating-point evaluation can be enforced by using float:


Example 2

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





An arithmetical expression specifying the parameter.

Return Values

Arithmetical expression.

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