WeierstrassHalfPeriodW3
WeierstrassHalfPeriodW3[{g2,g3}]
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.
Examples
open allclose allBasic Examples (3)
Scope (6)
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:
TraditionalForm formatting:
Properties & Relations (3)
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:
WeierstrassHalfPeriodW3 gives a zero of WeierstrassPPrime in the lattice cell:
Text
Wolfram Research (2017), WeierstrassHalfPeriodW3, Wolfram Language function, https://reference.wolfram.com/language/ref/WeierstrassHalfPeriodW3.html.
CMS
Wolfram Language. 2017. "WeierstrassHalfPeriodW3." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WeierstrassHalfPeriodW3.html.
APA
Wolfram Language. (2017). WeierstrassHalfPeriodW3. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WeierstrassHalfPeriodW3.html