# Fungrim entry: b10ca7

$\zeta\!\left(z, \tau\right) = \frac{1}{z} + \sum_{\left(m, n\right) \in {\mathbb{Z}}^{2} \setminus \left\{\left(0, 0\right)\right\}} \frac{1}{z - m - n \tau} + \frac{1}{m + n \tau} + \frac{z}{{\left(m + n \tau\right)}^{2}}$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; z \notin \Lambda_{(1, \tau)}$
TeX:
\zeta\!\left(z, \tau\right) = \frac{1}{z} + \sum_{\left(m, n\right) \in {\mathbb{Z}}^{2} \setminus \left\{\left(0, 0\right)\right\}} \frac{1}{z - m - n \tau} + \frac{1}{m + n \tau} + \frac{z}{{\left(m + n \tau\right)}^{2}}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; z \notin \Lambda_{(1, \tau)}
Definitions:
Fungrim symbol Notation Short description
WeierstrassZeta$\zeta\!\left(z, \tau\right)$ Weierstrass zeta function
Sum$\sum_{n} f(n)$ Sum
Pow${a}^{b}$ Power
ZZ$\mathbb{Z}$ Integers
CC$\mathbb{C}$ Complex numbers
HH$\mathbb{H}$ Upper complex half-plane
Lattice$\Lambda_{(a, b)}$ Complex lattice with periods a, b
Source code for this entry:
Entry(ID("b10ca7"),
Assumptions(And(Element(z, CC), Element(tau, HH), NotElement(z, Lattice(1, tau)))))