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# 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
Zeros$\mathop{\operatorname{zeros}\,}\limits_{P\left(x\right)} f\!\left(x\right)$ Zeros (roots) of function
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), Var(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

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

2019-09-19 20:12:49.583742 UTC