# Fungrim entry: f7a534

Symbol: WeierstrassP $\wp\!\left(z, \tau\right)$ Weierstrass elliptic function
Domain Codomain
Numbers
$z \in \mathbb{C} \setminus \Lambda_{(1, \tau)} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}$ $\wp\!\left(z, \tau\right) \in \mathbb{C}$
$z \in \Lambda_{(1, \tau)} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}$ $\wp\!\left(z, \tau\right) \in \left\{{\tilde \infty}\right\}$
Table data: $\left(P, Q\right)$ such that $\left(P\right) \implies \left(Q\right)$
Definitions:
Fungrim symbol Notation Short description
WeierstrassP$\wp\!\left(z, \tau\right)$ Weierstrass elliptic function
CC$\mathbb{C}$ Complex numbers
Lattice$\Lambda_{(a, b)}$ Complex lattice with periods a, b
HH$\mathbb{H}$ Upper complex half-plane
UnsignedInfinity${\tilde \infty}$ Unsigned infinity
Source code for this entry:
Entry(ID("f7a534"),
SymbolDefinition(WeierstrassP, WeierstrassP(z, tau), "Weierstrass elliptic function"),
Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(TableSection("Numbers"), Tuple(And(Element(z, SetMinus(CC, Lattice(1, tau))), Element(tau, HH)), Element(WeierstrassP(z, tau), CC)), Tuple(And(Element(z, Lattice(1, tau)), Element(tau, HH)), Element(WeierstrassP(z, tau), Set(UnsignedInfinity))))))

## Topics using this entry

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

2019-12-30 15:00:46.909060 UTC