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Fungrim entry: 12a9e8

℘ ⁣(−z,τ)=℘ ⁣(z,τ)\wp\!\left(-z, \tau\right) = \wp\!\left(z, \tau\right)
Assumptions:z∈C and⁡ τ∈H and⁡ z∉Λ(1,τ)z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, z \notin \Lambda_{(1, \tau)}
TeX:
\wp\!\left(-z, \tau\right) = \wp\!\left(z, \tau\right)

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, z \notin \Lambda_{(1, \tau)}
Definitions:
Fungrim symbol Notation Short description
WeierstrassP℘ ⁣(z,τ)\wp\!\left(z, \tau\right) Weierstrass elliptic function
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
LatticeΛ(a,b)\Lambda_{(a, b)} Complex lattice with periods a, b
Source code for this entry:
Entry(ID("12a9e8"),
    Formula(Equal(WeierstrassP(Neg(z), tau), WeierstrassP(z, tau))),
    Variables(z, tau),
    Assumptions(And(Element(z, CC), Element(tau, HH), NotElement(z, Lattice(1, tau)))))

Topics using this entry

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

2019-06-18 07:49:59.356594 UTC