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Fungrim entry: 5cdae6

θ1 ⁣(z+n,τ)=(1)nθ1 ⁣(z,τ)\theta_{1}\!\left(z + n , \tau\right) = {\left(-1\right)}^{n} \theta_{1}\!\left(z , \tau\right)
Assumptions:zCandτHandnZz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
TeX:
\theta_{1}\!\left(z + n , \tau\right) = {\left(-1\right)}^{n} \theta_{1}\!\left(z , \tau\right)

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("5cdae6"),
    Formula(Equal(JacobiTheta(1, Add(z, n), tau), Mul(Pow(-1, n), JacobiTheta(1, z, tau)))),
    Variables(z, tau, n),
    Assumptions(And(Element(z, CC), Element(tau, HH), Element(n, ZZ))))

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

2019-09-22 15:43:45.410764 UTC