# Fungrim entry: de9f42

$\sigma\!\left(z + \tau, \tau\right) = -\exp\!\left(2 \left(z + \frac{\tau}{2}\right) \zeta\!\left(\frac{\tau}{2}, \tau\right)\right) \sigma\!\left(z, \tau\right)$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}$
TeX:
\sigma\!\left(z + \tau, \tau\right) = -\exp\!\left(2 \left(z + \frac{\tau}{2}\right) \zeta\!\left(\frac{\tau}{2}, \tau\right)\right) \sigma\!\left(z, \tau\right)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
WeierstrassSigma$\sigma\!\left(z, \tau\right)$ Weierstrass sigma function
Exp${e}^{z}$ Exponential function
WeierstrassZeta$\zeta\!\left(z, \tau\right)$ Weierstrass zeta function
CC$\mathbb{C}$ Complex numbers
HH$\mathbb{H}$ Upper complex half-plane
Source code for this entry:
Entry(ID("de9f42"),
Formula(Equal(WeierstrassSigma(Add(z, tau), tau), Neg(Mul(Exp(Mul(Mul(2, Add(z, Div(tau, 2))), WeierstrassZeta(Div(tau, 2), tau))), WeierstrassSigma(z, tau))))),
Variables(z, tau),
Assumptions(And(Element(z, CC), Element(tau, HH))))

## Topics using this entry

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

2021-03-15 19:12:00.328586 UTC