Fungrim symbol: WeierstrassZeta

Symbol: WeierstrassZeta —

\zeta\!\left(z, \tau\right)

— Weierstrass zeta function

Domain	Codomain
Numbers
$z \in \mathbb{C} \setminus \Lambda_{(1, \tau)} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}$	$\zeta\!\left(z, \tau\right) \in \mathbb{C}$
$z \in \Lambda_{(1, \tau)} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}$	$\zeta\!\left(z, \tau\right) \in \left\{{\tilde \infty}\right\}$

Table data:

\left(P, Q\right)

such that

\left(P\right) \;\implies\; \left(Q\right)

Definitions:

Fungrim symbol	Notation	Short description
`WeierstrassZeta`	$\zeta\!\left(z, \tau\right)$	Weierstrass zeta 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("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 symbol

The symbol WeierstrassZeta appears in 5 topics:

Weierstrass elliptic functions (in 13 entries)
Eisenstein series (in 3 entries)
Modular lambda function (in 1 entries)
Jacobi theta functions (in 1 entries)
Dedekind eta function (in 1 entries)

Entries using this symbol

The symbol WeierstrassZeta appears in 17 entries: