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Fungrim entry: e6b579

lim⁡τ→i∞θ1 ⁣(z,τ)=0\lim_{\tau \to i \infty} \theta_{1}\!\left(z , \tau\right) = 0
Assumptions:z∈Cz \in \mathbb{C}
TeX:
\lim_{\tau \to i \infty} \theta_{1}\!\left(z , \tau\right) = 0

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
ComplexLimitlim⁡z→af(z)\lim_{z \to a} f(z) Limiting value, complex variable
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
ConstIii Imaginary unit
Infinity∞\infty Positive infinity
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("e6b579"),
    Formula(Equal(ComplexLimit(JacobiTheta(1, z, tau), For(tau, Mul(ConstI, Infinity))), 0)),
    Variables(z),
    Assumptions(Element(z, CC)))

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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