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Fungrim entry: ae6718

∫0∞(θ1′ ⁣(0,it))2 dt=(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
Integral∫abf(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)))))

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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