Fungrim entry: 72f583

\theta_{3}\!\left(0 , 7 i\right) = \left[\sqrt{\frac{\sqrt{13 + \sqrt{7}} + \sqrt{7 + 3 \sqrt{7}}}{14} {\left(28\right)}^{1 / 8}}\right] \theta_{3}\!\left(0 , i\right)

References:

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

TeX:

\theta_{3}\!\left(0 , 7 i\right) = \left[\sqrt{\frac{\sqrt{13 + \sqrt{7}} + \sqrt{7 + 3 \sqrt{7}}}{14} {\left(28\right)}^{1 / 8}}\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("72f583"),
    Formula(Equal(JacobiTheta(3, 0, Mul(7, ConstI)), Mul(Brackets(Sqrt(Mul(Div(Add(Sqrt(Add(13, Sqrt(7))), Sqrt(Add(7, Mul(3, Sqrt(7))))), 14), Pow(Parentheses(28), Div(1, 8))))), 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