Fungrim entry: 5f3210

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 entry

Weierstrass elliptic functions

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC