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Fungrim entry: ab1c77

θ42 ⁣(0,τ)=n=1cos ⁣(π(τ+1)n)\theta_{4}^{2}\!\left(0, \tau\right) = \sum_{n=-\infty}^{\infty} \frac{1}{\cos\!\left(\pi \left(\tau + 1\right) n\right)}
Assumptions:τH\tau \in \mathbb{H}
\theta_{4}^{2}\!\left(0, \tau\right) = \sum_{n=-\infty}^{\infty} \frac{1}{\cos\!\left(\pi \left(\tau + 1\right) 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(4, 0, tau), 2), Sum(Div(1, Cos(Mul(Mul(Pi, Add(tau, 1)), n))), For(n, Neg(Infinity), Infinity)))),
    Assumptions(Element(tau, HH)))

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2021-03-15 19:12:00.328586 UTC