Jacobi amplitude function am

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jacobiAM(u,m) represents the Jacobi amplitude function which is defined as the solution of .

The Jacobi amplitude is defined for complex arguments u and m.

Exact results are returned for m = 0, m = 1 or u = 0. In all other cases an unevaluated symbolic call is returned.

A floating-point value is computed if both arguments are numerical and at least one is a floating-point number.

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

Most calls with exact arguments are returned evaluated:

jacobiAM(PI/3, 1/2)

If m = 0, m = 1 or u = 0, an exact result is returned:

jacobiAM(PI/2, 0)

jacobiAM(2, 1)

jacobiAM(0, 1/2)



An arithmetical expression.


An arithmetical expression specifying the parameter.

Return Values

Arithmetical expression.

See Also

MuPAD Functions