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Fungrim entry: ae2c5d

poles⁡ z∈C℘ ⁣(z,τ)=Λ(1,τ)\mathop{\operatorname{poles}\,}\limits_{z \in \mathbb{C}} \wp\!\left(z, \tau\right) = \Lambda_{(1, \tau)}
Assumptions:τ∈H\tau \in \mathbb{H}
TeX:
\mathop{\operatorname{poles}\,}\limits_{z \in \mathbb{C}} \wp\!\left(z, \tau\right) = \Lambda_{(1, \tau)}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
WeierstrassP℘ ⁣(z,τ)\wp\!\left(z, \tau\right) Weierstrass elliptic 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("ae2c5d"),
    Formula(Equal(Poles(WeierstrassP(z, tau), ForElement(z, CC)), Lattice(1, tau))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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2021-03-15 19:12:00.328586 UTC