Fungrim entry: a95b7e

\wp\!\left(z + m + n \tau, \tau\right) = \wp\!\left(z, \tau\right)

Assumptions:

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}

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`	$\wp\!\left(z, \tau\right)$	Weierstrass elliptic function
`CC`	$\mathbb{C}$	Complex numbers
`HH`	$\mathbb{H}$	Upper complex half-plane
`Lattice`	$\Lambda_{(a, b)}$	Complex lattice with periods a, b
`ZZ`	$\mathbb{Z}$	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

Weierstrass elliptic functions