Fungrim entry: 69be32

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 entry

Weierstrass elliptic functions