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Fungrim entry: 9b7d8c

θ22 ⁣(0,τ)=∑n=−∞∞1cos⁡ ⁣(πτ(n+12))\theta_{2}^{2}\!\left(0, \tau\right) = \sum_{n=-\infty}^{\infty} \frac{1}{\cos\!\left(\pi \tau \left(n + \frac{1}{2}\right)\right)}
Assumptions:τ∈H\tau \in \mathbb{H}
TeX:
\theta_{2}^{2}\!\left(0, \tau\right) = \sum_{n=-\infty}^{\infty} \frac{1}{\cos\!\left(\pi \tau \left(n + \frac{1}{2}\right)\right)}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
Sum∑nf(n)\sum_{n} f(n) Sum
Coscos⁡(z)\cos(z) Cosine
Piπ\pi The constant pi (3.14...)
Infinity∞\infty Positive infinity
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("9b7d8c"),
    Formula(Equal(Pow(JacobiTheta(2, 0, tau), 2), Sum(Div(1, Cos(Mul(Mul(Pi, tau), Add(n, Div(1, 2))))), For(n, Neg(Infinity), Infinity)))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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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