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# Fungrim entry: ae6718

$\int_{0}^{\infty} {\left(\theta'_{1}\!\left(0 , i t\right)\right)}^{2} \, dt = \frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{4}}{4 \pi}$
TeX:
\int_{0}^{\infty} {\left(\theta'_{1}\!\left(0 , i t\right)\right)}^{2} \, dt = \frac{{\left(\Gamma\!\left(\frac{1}{4}\right)\right)}^{4}}{4 \pi}
Definitions:
Fungrim symbol Notation Short description
Integral$\int_{a}^{b} f(x) \, dx$ Integral
Pow${a}^{b}$ Power
JacobiTheta$\theta_{j}\!\left(z , \tau\right)$ Jacobi theta function
ConstI$i$ Imaginary unit
Infinity$\infty$ Positive infinity
Gamma$\Gamma(z)$ Gamma function
Pi$\pi$ The constant pi (3.14...)
Source code for this entry:
Entry(ID("ae6718"),
Formula(Equal(Integral(Pow(JacobiTheta(1, 0, Mul(ConstI, t), 1), 2), For(t, 0, Infinity)), Div(Pow(Gamma(Div(1, 4)), 4), Mul(4, Pi)))))

## Topics using this entry

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