Fungrim symbol: WeierstrassP

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 symbol

The symbol WeierstrassP appears in 5 topics:

Weierstrass elliptic functions (in 14 entries)
Modular lambda function (in 1 entries)
Jacobi theta functions (in 1 entries)
Eisenstein series (in 1 entries)
Carlson symmetric elliptic integrals (in 1 entries)

Entries using this symbol

The symbol WeierstrassP appears in 15 entries: