# Fungrim entry: 963daf

$\int_{0}^{\infty} \frac{\theta_{4}^{2}\!\left(0, i t\right)}{1 + {t}^{2}} \, dt = 1$
References:
• https://math.stackexchange.com/questions/1760270/closed-form-of-an-integral-involving-a-jacobi-theta-function-int-0-infty
TeX:
\int_{0}^{\infty} \frac{\theta_{4}^{2}\!\left(0, i t\right)}{1 + {t}^{2}} \, dt = 1
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
Source code for this entry:
Entry(ID("963daf"),
Formula(Equal(Integral(Div(Pow(JacobiTheta(4, 0, Mul(ConstI, t)), 2), Add(1, Pow(t, 2))), For(t, 0, Infinity)), 1)),
References("https://math.stackexchange.com/questions/1760270/closed-form-of-an-integral-involving-a-jacobi-theta-function-int-0-infty"))

## 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