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Fungrim entry: 6021ba

Poles ⁣(ζ ⁣(z,τ),z,C)=Λ(1,τ)\operatorname{Poles}\!\left(\zeta\!\left(z, \tau\right), z, \mathbb{C}\right) = \Lambda_{(1, \tau)}
Assumptions:τH\tau \in \mathbb{H}
TeX:
\operatorname{Poles}\!\left(\zeta\!\left(z, \tau\right), z, \mathbb{C}\right) = \Lambda_{(1, \tau)}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
WeierstrassZetaζ ⁣(z,τ)\zeta\!\left(z, \tau\right) Weierstrass zeta function
CCC\mathbb{C} Complex numbers
LatticeΛ(a,b)\Lambda_{(a, b)} Complex lattice with periods a, b
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("6021ba"),
    Formula(Equal(Poles(WeierstrassZeta(z, tau), z, CC), Lattice(1, tau))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-15 14:14:26.267625 UTC