Fungrim symbol: WeierstrassSigma

Symbol: WeierstrassSigma —

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

— Weierstrass sigma function

Domain	Codomain
Numbers
$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}$	$\sigma\!\left(z, \tau\right) \in \mathbb{C}$

Table data:

\left(P, Q\right)

such that

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

Definitions:

Fungrim symbol	Notation	Short description
`WeierstrassSigma`	$\sigma\!\left(z, \tau\right)$	Weierstrass sigma function
`CC`	$\mathbb{C}$	Complex numbers
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("5f3210"),
    SymbolDefinition(WeierstrassSigma, WeierstrassSigma(z, tau), "Weierstrass sigma function"),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(TableSection("Numbers"), Tuple(And(Element(z, CC), Element(tau, HH)), Element(WeierstrassSigma(z, tau), CC)))))

Topics using this symbol

The symbol WeierstrassSigma appears in 2 topics:

Weierstrass elliptic functions (in 9 entries)
Jacobi theta functions (in 1 entries)

Entries using this symbol

The symbol WeierstrassSigma appears in 9 entries: