Fungrim home page

Fungrim entry: f7a534

Symbol: WeierstrassP  ⁣(z,τ)\wp\!\left(z, \tau\right) Weierstrass elliptic function
Domain Codomain
Numbers
zCΛ(1,τ)  and  τHz \in \mathbb{C} \setminus \Lambda_{(1, \tau)} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}  ⁣(z,τ)C\wp\!\left(z, \tau\right) \in \mathbb{C}
zΛ(1,τ)  and  τHz \in \Lambda_{(1, \tau)} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}  ⁣(z,τ){~}\wp\!\left(z, \tau\right) \in \left\{{\tilde \infty}\right\}
Table data: (P,Q)\left(P, Q\right) such that (P)        (Q)\left(P\right) \;\implies\; \left(Q\right)
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
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.

2021-03-15 19:12:00.328586 UTC