Fungrim entry: f7a534

Symbol: WeierstrassP —

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

— Weierstrass elliptic function

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

Table data:

\left(P, Q\right)

such that

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

Definitions:

Fungrim symbol	Notation	Short description
`WeierstrassP`	$\wp\!\left(z, \tau\right)$	Weierstrass elliptic 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("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

Weierstrass elliptic functions