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

Specific values of Jacobi theta functions