Fungrim home page

Fungrim entry: a95b7e

 ⁣(z+m+nτ,τ)= ⁣(z,τ)\wp\!\left(z + m + n \tau, \tau\right) = \wp\!\left(z, \tau\right)
Assumptions:zCandτHandzΛ(1,τ)andmZandnZz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, z \notin \Lambda_{(1, \tau)} \,\mathbin{\operatorname{and}}\, m \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
TeX:
\wp\!\left(z + m + n \tau, \tau\right) = \wp\!\left(z, \tau\right)

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, z \notin \Lambda_{(1, \tau)} \,\mathbin{\operatorname{and}}\, m \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
WeierstrassP ⁣(z,τ)\wp\!\left(z, \tau\right) Weierstrass elliptic function
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
LatticeΛ(a,b)\Lambda_{(a, b)} Complex lattice with periods a, b
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("a95b7e"),
    Formula(Equal(WeierstrassP(Add(Add(z, m), Mul(n, tau)), tau), WeierstrassP(z, tau))),
    Variables(z, tau, m, n),
    Assumptions(And(Element(z, CC), Element(tau, HH), NotElement(z, Lattice(1, tau)), Element(m, ZZ), Element(n, ZZ))))

Topics using this entry

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

2019-09-15 14:14:26.267625 UTC