Jacobi elliptic function dn
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jacobiDN(u,m) represents the Jacobi elliptic
Let . Then the Jacobi elliptic function dn 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.
When called with floating-point arguments, these functions are
sensitive to the environment variable
DIGITS which determines
the numerical working precision.
For most arguments, the Jacobi 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
For m = 0, the result is a constant:
For m = 1, the result is expressed using a trigonometric function:
An arithmetical expression specifying the parameter.