gives the value η1 of the Weierstrass zeta function ζ at the half-period TemplateBox[{{g, _, 2}, {g, _, 3}}, WeierstrassHalfPeriodW1].


  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • WeierstrassEta1 can be evaluated to arbitrary numerical precision.


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Basic Examples  (3)

Represent the value of WeierstrassZeta at the half-period ω1:

Evaluate numerically:

Plot the real and imaginary parts of η1:

Scope  (4)

Evaluate for complex arguments:

Evaluate to arbitrary numerical precision:

Precision of the output tracks the precision of the input:

TraditionalForm formatting:

Properties & Relations  (2)

WeierstrassZeta is quasiperiodic on the lattice of periods of WeierstrassP:

Values of WeierstrassZeta at half-periods are not linearly independent:

This identity holds for all arguments:

Introduced in 2017