Fungrim entry: c6234b

\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} \wp\!\left(z, i\right) = \left\{ \left(m + \frac{1}{2}\right) + \left(n + \frac{1}{2}\right) i : m \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z} \right\}

TeX:

\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} \wp\!\left(z, i\right) = \left\{ \left(m + \frac{1}{2}\right) + \left(n + \frac{1}{2}\right) i : m \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z} \right\}

Definitions:

Fungrim symbol	Notation	Short description
`WeierstrassP`	$\wp\!\left(z, \tau\right)$	Weierstrass elliptic function
`ConstI`	$i$	Imaginary unit
`CC`	$\mathbb{C}$	Complex numbers
`SetBuilder`	$\left\{ f\!\left(x\right) : P\!\left(x\right) \right\}$	Set comprehension
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("c6234b"),
    Formula(Equal(Zeros(WeierstrassP(z, ConstI), z, Element(z, CC)), SetBuilder(Add(Parentheses(Add(m, Div(1, 2))), Mul(Add(n, Div(1, 2)), ConstI)), Tuple(m, n), And(Element(m, ZZ), Element(n, ZZ))))))

Topics using this entry

Weierstrass elliptic functions