![TemplateBox[{{g, _, 2}, {g, _, 3}}, WeierstrassHalfPeriodW3]](Files/WeierstrassEta3.en/3.png "TemplateBox[{{g, _, 2}, {g, _, 3}}, WeierstrassHalfPeriodW3]"){kind=small}
WeierstrassEta3
WeierstrassEta3[{g2,g3}]
gives the value η3 of the Weierstrass zeta function ζ at the half-period ![TemplateBox[{{g, _, 2}, {g, _, 3}}, WeierstrassHalfPeriodW3]](Files/WeierstrassEta3.en/1.png "TemplateBox[{{g, _, 2}, {g, _, 3}}, WeierstrassHalfPeriodW3]"){kind=small}
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Details
- Mathematical function, suitable for both symbolic and numerical manipulation.
- WeierstrassEta3 can be evaluated to arbitrary numerical precision.
Examples
open all close allBasic Examples (3)
Represent the value of WeierstrassZeta at the half-period ω3:
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:
WeierstrassEta3 has both singularities and discontinuities:
WeierstrassEta3 is neither non-negative nor non-positive:
WeierstrassEta3 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:
Text
Wolfram Research (2017), WeierstrassEta3, Wolfram Language function, https://reference.wolfram.com/language/ref/WeierstrassEta3.html.
CMS
Wolfram Language. 2017. "WeierstrassEta3." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WeierstrassEta3.html.
APA
Wolfram Language. (2017). WeierstrassEta3. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WeierstrassEta3.html