# Fungrim entry: c60033

$\theta_{3}\!\left(0 , \sqrt{6} i\right) = {\left(\frac{\sqrt{6}}{96 {\pi}^{3}} \frac{\Gamma\!\left(\frac{1}{24}\right) \Gamma\!\left(\frac{5}{24}\right) \Gamma\!\left(\frac{7}{24}\right) \Gamma\!\left(\frac{11}{24}\right)}{18 + 12 \sqrt{2} - 10 \sqrt{3} - 7 \sqrt{6}}\right)}^{1 / 4}$
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
JacobiTheta$\theta_{j}\!\left(z , \tau\right)$ Jacobi theta function
Sqrt$\sqrt{z}$ Principal square root
ConstI$i$ Imaginary unit
Pow${a}^{b}$ Power
Pi$\pi$ The constant pi (3.14...)
Gamma$\Gamma(z)$ 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.

2021-03-15 19:12:00.328586 UTC