WeierstrassHalfPeriodW2

WeierstrassHalfPeriodW2[{g2,g3}]

gives the half-period ω2 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.
  • WeierstrassHalfPeriodW2 can be evaluated to arbitrary precision.

Examples

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Basic Examples  (3)

Evaluate numerically:

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

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

Scope  (3)

Evaluate to arbitrary precision:

Precision of the output tracks the precision of the input:

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:

WeierstrassHalfPeriodW2 gives a zero of WeierstrassPPrime in the lattice cell:

Wolfram Research (2017), WeierstrassHalfPeriodW2, Wolfram Language function, https://reference.wolfram.com/language/ref/WeierstrassHalfPeriodW2.html.

Text

Wolfram Research (2017), WeierstrassHalfPeriodW2, Wolfram Language function, https://reference.wolfram.com/language/ref/WeierstrassHalfPeriodW2.html.

BibTeX

@misc{reference.wolfram_2021_weierstrasshalfperiodw2, author="Wolfram Research", title="{WeierstrassHalfPeriodW2}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/WeierstrassHalfPeriodW2.html}", note=[Accessed: 20-September-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_weierstrasshalfperiodw2, organization={Wolfram Research}, title={WeierstrassHalfPeriodW2}, year={2017}, url={https://reference.wolfram.com/language/ref/WeierstrassHalfPeriodW2.html}, note=[Accessed: 20-September-2021 ]}

CMS

Wolfram Language. 2017. "WeierstrassHalfPeriodW2." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WeierstrassHalfPeriodW2.html.

APA

Wolfram Language. (2017). WeierstrassHalfPeriodW2. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WeierstrassHalfPeriodW2.html