# Fungrim entry: 35403b

$\sigma\!\left(z + 1, \tau\right) = -\exp\!\left(2 \left(z + \frac{1}{2}\right) \zeta\!\left(\frac{1}{2}, \tau\right)\right) \sigma\!\left(z, \tau\right)$
Assumptions:$z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}$
TeX:
\sigma\!\left(z + 1, \tau\right) = -\exp\!\left(2 \left(z + \frac{1}{2}\right) \zeta\!\left(\frac{1}{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("35403b"),
Formula(Equal(WeierstrassSigma(Add(z, 1), tau), Neg(Mul(Exp(Mul(Mul(2, Add(z, Div(1, 2))), WeierstrassZeta(Div(1, 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.

2019-12-30 15:00:46.909060 UTC