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Fungrim entry: 1403b5

θ3 ⁣(0,i)=Γ ⁣(14)2π3/4\theta_{3}\!\left(0 , i\right) = \frac{\Gamma\!\left(\frac{1}{4}\right)}{\sqrt{2} {\pi}^{3 / 4}}
TeX:
\theta_{3}\!\left(0 , i\right) = \frac{\Gamma\!\left(\frac{1}{4}\right)}{\sqrt{2} {\pi}^{3 / 4}}
Definitions:
Fungrim symbol Notation Short description
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
ConstIii Imaginary unit
GammaFunctionΓ ⁣(z)\Gamma\!\left(z\right) Gamma function
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
ConstPiπ\pi The constant pi (3.14...)
Source code for this entry:
Entry(ID("1403b5"),
    Formula(Equal(JacobiTheta(3, 0, ConstI), Div(GammaFunction(Div(1, 4)), Mul(Sqrt(2), Pow(ConstPi, Div(3, 4)))))))

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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