WeierstrassHalfPeriodW3

WeierstrassHalfPeriodW3[{g2,g3}]

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

Details

Examples

open allclose all

Basic Examples  (3)

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:

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:

Wolfram Research (2017), WeierstrassHalfPeriodW3, Wolfram Language function, https://reference.wolfram.com/language/ref/WeierstrassHalfPeriodW3.html.

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

BibTeX

@misc{reference.wolfram_2022_weierstrasshalfperiodw3, author="Wolfram Research", title="{WeierstrassHalfPeriodW3}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/WeierstrassHalfPeriodW3.html}", note=[Accessed: 26-November-2022 ]}

BibLaTeX

@online{reference.wolfram_2022_weierstrasshalfperiodw3, organization={Wolfram Research}, title={WeierstrassHalfPeriodW3}, year={2017}, url={https://reference.wolfram.com/language/ref/WeierstrassHalfPeriodW3.html}, note=[Accessed: 26-November-2022 ]}