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

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WeierstrassHalfPeriods

WeierstrassHalfPeriods[{g₂, g₃}]
gives the half-periods {

} for Weierstrass elliptic functions corresponding to the invariants {g₂, g₃}.

The half-periods {, } define the fundamental period parallelogram for the Weierstrass elliptic functions.

Evaluate numerically:

Given the half-periods, calculate a value of a Weierstrass

function:

Evaluate numerically:

Given the half-periods, calculate a value of a Weierstrass

function:

Evaluate to high precision:

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

Plot an elliptic function over a period parallelogram:

WeierstrassHalfPeriods is effectively the inverse of WeierstrassHalfInvariants:

Assignment to half-periods with symbolic or exact invariants is impossible as the right-hand side is not a list:

A doubly periodic function over the complex plane: