Fungrim entry: 69eb9b

\operatorname{HolomorphicDomain}\!\left(\wp\!\left(z, \tau\right), z, \mathbb{C}\right) = \mathbb{C} \setminus \Lambda_{(1, \tau)}

Assumptions:

\tau \in \mathbb{H}

TeX:

\operatorname{HolomorphicDomain}\!\left(\wp\!\left(z, \tau\right), z, \mathbb{C}\right) = \mathbb{C} \setminus \Lambda_{(1, \tau)}

\tau \in \mathbb{H}

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

Source code for this entry:

Entry(ID("69eb9b"),
    Formula(Equal(HolomorphicDomain(WeierstrassP(z, tau), z, CC), SetMinus(CC, Lattice(1, tau)))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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.

2019-06-18 07:49:59.356594 UTC