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Fungrim entry: 69be32

Symbol: WeierstrassZeta ζ ⁣(z,τ)\zeta\!\left(z, \tau\right) Weierstrass zeta function
Domain Codomain
zCΛ(1,τ)  and  τHz \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)  and  τHz \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)
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:
    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))))))

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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