Fungrim home page

Fungrim entry: 69be32

Symbol: WeierstrassZeta ζ ⁣(z,τ)\zeta\!\left(z, \tau\right) Weierstrass zeta function
Domain Codomain
Numbers
zCΛ(1,τ)andτHz \in \mathbb{C} \setminus \Lambda_{(1, \tau)} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} ζ ⁣(z,τ)C\zeta\!\left(z, \tau\right) \in \mathbb{C}
zΛ(1,τ)andτHz \in \Lambda_{(1, \tau)} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} ζ ⁣(z,τ){~}\zeta\!\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
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
UnsignedInfinity~{\tilde \infty} Unsigned infinity
Source code for this entry:
Entry(ID("69be32"),
    SymbolDefinition(WeierstrassZeta, WeierstrassZeta(z, tau), "Weierstrass zeta 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(WeierstrassZeta(z, tau), CC)), Tuple(And(Element(z, Lattice(1, tau)), Element(tau, HH)), Element(WeierstrassZeta(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.

2019-06-18 07:49:59.356594 UTC