WeierstrassEta1

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

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

Evaluate numerically:

Plot the real and imaginary parts of η₁:

Evaluate for complex arguments:

Evaluate to arbitrary numerical precision:

Precision of the output tracks the precision of the input:

WeierstrassZeta is quasi‐periodic on the lattice of periods of WeierstrassP:

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

This identity holds for all arguments:

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