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Mathematica > Mathematics and Algorithms > Mathematical Functions > Special Functions > Elliptic Functions >

Built-in Mathematica Symbol

InverseWeierstrassP

InverseWeierstrassP[p, {g₂, g₃}]
gives a value of u for which the Weierstrass function

is equal to p.

The value of u returned always lies in the fundamental period parallelogram defined by the complex half-periods and .

InverseWeierstrassP[{p, q}, {g₂, g₃}] finds the unique value of u for which and . For such a value to exist, p and q must be related by .

Evaluate numerically:

Evaluate for complex arguments and parameters:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Evaluate the generalized form numerically:

These are the inverse relationships with WeierstrassP and WeierstrassPPrime:

Plot the real and imaginary part of InverseWeierstrassP:

Form derivatives:

If the first argument does not represent a pair of values of Weierstrass

functions, InverseWeierstrassP stays unevaluated:

InverseWeierstrassP evaluates to a vector-valued first argument: