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

Specific values of Jacobi theta functions