Fungrim home page

Fungrim entry: a0c85d

ζ ⁣(z+τ,τ)=ζ ⁣(z,τ)+ζ ⁣(τ2,τ)\zeta\!\left(z + \tau, \tau\right) = \zeta\!\left(z, \tau\right) + \zeta\!\left(\frac{\tau}{2}, \tau\right)
Assumptions:zC  and  τH  and  zΛ(1,τ)z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; z \notin \Lambda_{(1, \tau)}
\zeta\!\left(z + \tau, \tau\right) = \zeta\!\left(z, \tau\right) + \zeta\!\left(\frac{\tau}{2}, \tau\right)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; z \notin \Lambda_{(1, \tau)}
Fungrim symbol Notation Short description
WeierstrassZetaζ ⁣(z,τ)\zeta\!\left(z, \tau\right) Weierstrass zeta function
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
LatticeΛ(a,b)\Lambda_{(a, b)} Complex lattice with periods a, b
Source code for this entry:
    Formula(Equal(WeierstrassZeta(Add(z, tau), tau), Add(WeierstrassZeta(z, tau), WeierstrassZeta(Div(tau, 2), tau)))),
    Variables(z, tau),
    Assumptions(And(Element(z, CC), Element(tau, HH), NotElement(z, Lattice(1, tau)))))

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