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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}
\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}
Fungrim symbol Notation Short description
Integralabf ⁣(x)dx\int_{a}^{b} f\!\left(x\right) \, 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
GammaFunctionΓ ⁣(z)\Gamma\!\left(z\right) Gamma function
ConstPiπ\pi The constant pi (3.14...)
Source code for this entry:
    Formula(Equal(Integral(Pow(JacobiTheta(1, 0, Mul(ConstI, t), 1), 2), Tuple(t, 0, Infinity)), Div(Pow(GammaFunction(Div(1, 4)), 4), Mul(4, ConstPi)))))

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

2019-09-22 15:43:45.410764 UTC