Fungrim home page

Fungrim entry: c60033

θ3 ⁣(0,6i)=(696π3Γ ⁣(124)Γ ⁣(524)Γ ⁣(724)Γ ⁣(1124)18+12210376)1/4\theta_{3}\!\left(0 , \sqrt{6} i\right) = {\left(\frac{\sqrt{6}}{96 {\pi}^{3}} \frac{\Gamma\!\left(\frac{1}{24}\right) \Gamma\!\left(\frac{5}{24}\right) \Gamma\!\left(\frac{7}{24}\right) \Gamma\!\left(\frac{11}{24}\right)}{18 + 12 \sqrt{2} - 10 \sqrt{3} - 7 \sqrt{6}}\right)}^{1 / 4}
References:
  • http://mathworld.wolfram.com/PolyasRandomWalkConstants.html
TeX:
\theta_{3}\!\left(0 , \sqrt{6} i\right) = {\left(\frac{\sqrt{6}}{96 {\pi}^{3}} \frac{\Gamma\!\left(\frac{1}{24}\right) \Gamma\!\left(\frac{5}{24}\right) \Gamma\!\left(\frac{7}{24}\right) \Gamma\!\left(\frac{11}{24}\right)}{18 + 12 \sqrt{2} - 10 \sqrt{3} - 7 \sqrt{6}}\right)}^{1 / 4}
Definitions:
Fungrim symbol Notation Short description
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
Sqrtz\sqrt{z} Principal square root
ConstIii Imaginary unit
Powab{a}^{b} Power
Piπ\pi The constant pi (3.14...)
GammaΓ(z)\Gamma(z) Gamma function
Source code for this entry:
Entry(ID("c60033"),
    Formula(Equal(JacobiTheta(3, 0, Mul(Sqrt(6), ConstI)), Pow(Mul(Div(Sqrt(6), Mul(96, Pow(Pi, 3))), Div(Mul(Mul(Mul(Gamma(Div(1, 24)), Gamma(Div(5, 24))), Gamma(Div(7, 24))), Gamma(Div(11, 24))), Sub(Sub(Add(18, Mul(12, Sqrt(2))), Mul(10, Sqrt(3))), Mul(7, Sqrt(6))))), Div(1, 4)))),
    References("http://mathworld.wolfram.com/PolyasRandomWalkConstants.html"))

Topics using this entry

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

2020-01-31 18:09:28.494564 UTC