WeierstrassHalfPeriodW2

WeierstrassHalfPeriodW2[{g2,g3}]

gives the half-period ω2 for the Weierstrass elliptic functions corresponding to the invariants {g2,g3}.

Details

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  (8)

Evaluate to arbitrary precision:

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

Evaluate symbolically for the equianharmonic case:

Evaluate symbolically for the lemniscatic case:

WeierstrassHalfPeriodW2 has both singularities and discontinuities:

WeierstrassHalfPeriodW2 is neither non-negative nor non-positive:

WeierstrassHalfPeriodW2 is neither convex nor concave:

WeierstrassHalfPeriodW2 can be used with CenteredInterval objects:

TraditionalForm formatting:

Properties & Relations  (4)

Up to a change in sign, the half-period is equal to the sum of the half-periods and :

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

The half-periods , and of Weierstrass elliptic functions 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 (updated 2023).

Text

Wolfram Research (2017), WeierstrassHalfPeriodW2, Wolfram Language function, https://reference.wolfram.com/language/ref/WeierstrassHalfPeriodW2.html (updated 2023).

CMS

Wolfram Language. 2017. "WeierstrassHalfPeriodW2." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. 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

BibTeX

@misc{reference.wolfram_2024_weierstrasshalfperiodw2, author="Wolfram Research", title="{WeierstrassHalfPeriodW2}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/WeierstrassHalfPeriodW2.html}", note=[Accessed: 19-June-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_weierstrasshalfperiodw2, organization={Wolfram Research}, title={WeierstrassHalfPeriodW2}, year={2023}, url={https://reference.wolfram.com/language/ref/WeierstrassHalfPeriodW2.html}, note=[Accessed: 19-June-2024 ]}