Fungrim entry: 6ade92

\theta_{3}\!\left(0 , 45 i\right) = \left[\frac{3 + \sqrt{5} + \left(\sqrt{3} + \sqrt{5} + {60}^{1 / 4}\right) {\left(2 + \sqrt{3}\right)}^{1 / 3}}{3 \sqrt{10 + 10 \sqrt{5}}}\right] \theta_{3}\!\left(0 , i\right)

References:

https://doi.org/10.1016/j.jmaa.2003.12.009

TeX:

\theta_{3}\!\left(0 , 45 i\right) = \left[\frac{3 + \sqrt{5} + \left(\sqrt{3} + \sqrt{5} + {60}^{1 / 4}\right) {\left(2 + \sqrt{3}\right)}^{1 / 3}}{3 \sqrt{10 + 10 \sqrt{5}}}\right] \theta_{3}\!\left(0 , i\right)

Definitions:

Fungrim symbol	Notation	Short description
`JacobiTheta`	$\theta_{j}\!\left(z , \tau\right)$	Jacobi theta function
`ConstI`	$i$	Imaginary unit
`Sqrt`	$\sqrt{z}$	Principal square root
`Pow`	${a}^{b}$	Power

Source code for this entry:

Entry(ID("6ade92"),
    Formula(Equal(JacobiTheta(3, 0, Mul(45, ConstI)), Mul(Brackets(Div(Add(Add(3, Sqrt(5)), Mul(Add(Add(Sqrt(3), Sqrt(5)), Pow(60, Div(1, 4))), Pow(Add(2, Sqrt(3)), Div(1, 3)))), Mul(3, Sqrt(Add(10, Mul(10, Sqrt(5))))))), JacobiTheta(3, 0, ConstI)))),
    References("https://doi.org/10.1016/j.jmaa.2003.12.009"))

Topics using this entry

Specific values of Jacobi theta functions