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Fungrim entry: a19141

θ3(2r+1) ⁣(0,τ)=0\theta^{(2 r + 1)}_{3}\!\left(0 , \tau\right) = 0
Assumptions:τ∈H  and⁡  r∈Z≥0\tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; r \in \mathbb{Z}_{\ge 0}
TeX:
\theta^{(2 r + 1)}_{3}\!\left(0 , \tau\right) = 0

\tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; r \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
HHH\mathbb{H} Upper complex half-plane
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("a19141"),
    Formula(Equal(JacobiTheta(3, 0, tau, Add(Mul(2, r), 1)), 0)),
    Variables(tau, r),
    Assumptions(And(Element(tau, HH), Element(r, ZZGreaterEqual(0)))))

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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