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# Fungrim entry: 799b5e

$\theta_{3}\!\left(0 , \sqrt{6} i\right) = \sqrt{\frac{2}{\pi} K\!\left({\left(2 - \sqrt{3}\right)}^{2} {\left(\sqrt{2} - \sqrt{3}\right)}^{2}\right)}$
References:
• http://mathworld.wolfram.com/PolyasRandomWalkConstants.html
TeX:
\theta_{3}\!\left(0 , \sqrt{6} i\right) = \sqrt{\frac{2}{\pi} K\!\left({\left(2 - \sqrt{3}\right)}^{2} {\left(\sqrt{2} - \sqrt{3}\right)}^{2}\right)}
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
Pi$\pi$ The constant pi (3.14...)
EllipticK$K(m)$ Legendre complete elliptic integral of the first kind
Pow${a}^{b}$ Power
Source code for this entry:
Entry(ID("799b5e"),
Formula(Equal(JacobiTheta(3, 0, Mul(Sqrt(6), ConstI)), Sqrt(Mul(Div(2, Pi), EllipticK(Mul(Pow(Sub(2, Sqrt(3)), 2), Pow(Sub(Sqrt(2), Sqrt(3)), 2))))))),
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