Fungrim home page

Fungrim entry: b46534

θ2 ⁣(z+2n,τ)=θ2 ⁣(z,τ)\theta_{2}\!\left(z + 2 n , \tau\right) = \theta_{2}\!\left(z , \tau\right)
Assumptions:zCandτHandnZz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
\theta_{2}\!\left(z + 2 n , \tau\right) = \theta_{2}\!\left(z , \tau\right)

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
Fungrim symbol Notation Short description
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Equal(JacobiTheta(2, Add(z, Mul(2, n)), tau), JacobiTheta(2, z, tau))),
    Variables(z, tau, n),
    Assumptions(And(Element(z, CC), Element(tau, HH), 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.

2019-11-19 15:10:20.037976 UTC