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Fungrim entry: 7b3ac4

θ32 ⁣(0,τ)=n=1cos ⁣(πτn)\theta_{3}^{2}\!\left(0, \tau\right) = \sum_{n=-\infty}^{\infty} \frac{1}{\cos\!\left(\pi \tau n\right)}
Assumptions:zCandτHz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}
TeX:
\theta_{3}^{2}\!\left(0, \tau\right) = \sum_{n=-\infty}^{\infty} \frac{1}{\cos\!\left(\pi \tau n\right)}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \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
Sumnf ⁣(n)\sum_{n} f\!\left(n\right) Sum
ConstPiπ\pi The constant pi (3.14...)
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("7b3ac4"),
    Formula(Equal(Pow(JacobiTheta(3, 0, tau), 2), Sum(Div(1, Cos(Mul(Mul(ConstPi, tau), n))), Tuple(n, Neg(Infinity), Infinity)))),
    Variables(tau),
    Assumptions(And(Element(z, CC), 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.

2019-09-19 20:12:49.583742 UTC