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Fungrim entry: 2faeb9

θ1 ⁣(z+2n,τ)=θ1 ⁣(z,τ)\theta_{1}\!\left(z + 2 n , \tau\right) = \theta_{1}\!\left(z , \tau\right)
Assumptions:zC  and  τH  and  nZz \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
\theta_{1}\!\left(z + 2 n , \tau\right) = \theta_{1}\!\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(1, Add(z, Mul(2, n)), tau), 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.

2021-03-15 19:12:00.328586 UTC