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Fungrim entry: f8cd8f

θ32 ⁣(0,τ)=1+2n=11cos ⁣(πτn)\theta_{3}^{2}\!\left(0, \tau\right) = 1 + 2 \sum_{n=1}^{\infty} \frac{1}{\cos\!\left(\pi \tau n\right)}
Assumptions:τH\tau \in \mathbb{H}
\theta_{3}^{2}\!\left(0, \tau\right) = 1 + 2 \sum_{n=1}^{\infty} \frac{1}{\cos\!\left(\pi \tau n\right)}

\tau \in \mathbb{H}
Fungrim symbol Notation Short description
Powab{a}^{b} Power
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
Sumnf(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:
    Formula(Equal(Pow(JacobiTheta(3, 0, tau), 2), Add(1, Mul(2, Sum(Div(1, Cos(Mul(Mul(Pi, tau), n))), For(n, 1, Infinity)))))),
    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