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Fungrim entry: 799b5e

θ3 ⁣(0,6i)=2πK ⁣((23)2(23)2)\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
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
Sqrtz\sqrt{z} Principal square root
ConstIii Imaginary unit
Piπ\pi The constant pi (3.14...)
EllipticKK(m)K(m) Legendre complete elliptic integral of the first kind
Powab{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"))

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2021-03-15 19:12:00.328586 UTC