Fungrim home page

Fungrim entry: ae6718

0(θ1 ⁣(0,it))2dt=(Γ ⁣(14))44π\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
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
Powab{a}^{b} Power
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
ConstIii Imaginary unit
Infinity\infty Positive infinity
GammaΓ(z)\Gamma(z) Gamma function
Piπ\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.

2019-11-19 15:10:20.037976 UTC