WeierstrassHalfPeriodW3

gives the half-period ω₃ for the Weierstrass elliptic functions corresponding to the invariants {g₂,g₃}.

Details

Mathematical function, suitable for both symbolic and numerical manipulation.
The half-periods define the fundamental period parallelogram for the Weierstrass elliptic functions.
WeierstrassHalfPeriodW3 gives the second element ω₃ returned by WeierstrassHalfPeriods.
WeierstrassHalfPeriodW3 can be evaluated to arbitrary precision.

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Evaluate numerically:

Plot the real and imaginary parts of the third half-period:

Compute the value of the Weierstrass function at the third half-period:

Evaluate to arbitrary precision:

Precision of the output tracks the precision of the input:

WeierstrassHalfPeriodW3 has both singularities and discontinuities:

WeierstrassHalfPeriodW3 is neither non-negative nor non-positive:

WeierstrassHalfPeriodW3 is neither convex nor concave:

WeierstrassP is periodic with periods equal to twice the half-periods:

Weierstrass half-periods , and are not linearly independent:

This identity holds for all arguments:

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