WeierstrassEta2 [{g2,g3}]
gives the value η2 of the Weierstrass zeta function ζ at the half-period TemplateBox[{{g, _, 2}, {g, _, 3}}, WeierstrassHalfPeriodW2].
WeierstrassEta2
WeierstrassEta2 [{g2,g3}]
gives the value η2 of the Weierstrass zeta function ζ at the half-period TemplateBox[{{g, _, 2}, {g, _, 3}}, WeierstrassHalfPeriodW2].
Details
- Mathematical function, suitable for both symbolic and numerical manipulation.
- WeierstrassEta2 can be evaluated to arbitrary numerical precision.
Examples
open all close allBasic Examples (3)
Represent the value of WeierstrassZeta at the half-period ω2:
Evaluate numerically:
Plot the real and imaginary parts of η2:
Scope (8)
Evaluate for complex arguments:
Evaluate to arbitrary numerical precision:
The precision of the output tracks the precision of the input:
Evaluate symbolically for the equianharmonic case:
Evaluate symbolically for the lemniscatic case:
WeierstrassEta2 has both singularities and discontinuities:
WeierstrassEta2 is neither non-negative nor non-positive:
It is inherently complex:
WeierstrassEta2 is neither convex nor concave:
TraditionalForm formatting:
Properties & Relations (2)
WeierstrassZeta is quasiperiodic on the lattice of periods of WeierstrassP :
The values of WeierstrassZeta at the half-periods are not linearly independent:
This identity holds for all arguments:
Related Guides
History
Text
Wolfram Research (2017), WeierstrassEta2, Wolfram Language function, https://reference.wolfram.com/language/ref/WeierstrassEta2.html.
CMS
Wolfram Language. 2017. "WeierstrassEta2." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WeierstrassEta2.html.
APA
Wolfram Language. (2017). WeierstrassEta2. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WeierstrassEta2.html
BibTeX
@misc{reference.wolfram_2025_weierstrasseta2, author="Wolfram Research", title="{WeierstrassEta2}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/WeierstrassEta2.html}", note=[Accessed: 10-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_weierstrasseta2, organization={Wolfram Research}, title={WeierstrassEta2}, year={2017}, url={https://reference.wolfram.com/language/ref/WeierstrassEta2.html}, note=[Accessed: 10-January-2026]}