Fungrim home page

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}
TeX:
\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}
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
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("f8cd8f"),
    Formula(Equal(Pow(JacobiTheta(3, 0, tau), 2), Add(1, Mul(2, Sum(Div(1, Cos(Mul(Mul(ConstPi, tau), n))), Tuple(n, 1, Infinity)))))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-20 18:07:53.062439 UTC