Fungrim entry: e2bc80

\theta_{3}\!\left(0 , 1 + 8 i\right) = \left[{2}^{-7 / 8} {\left(16 + 15 \cdot {2}^{1 / 4} + 12 \sqrt{2} + 9 \cdot {8}^{1 / 4}\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 , 1 + 8 i\right) = \left[{2}^{-7 / 8} {\left(16 + 15 \cdot  {2}^{1 / 4} + 12 \sqrt{2} + 9 \cdot  {8}^{1 / 4}\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
`Pow`	${a}^{b}$	Power
`Sqrt`	$\sqrt{z}$	Principal square root

Source code for this entry:

Entry(ID("e2bc80"),
    Formula(Equal(JacobiTheta(3, 0, Add(1, Mul(8, ConstI))), Mul(Brackets(Mul(Pow(2, Neg(Div(7, 8))), Pow(Add(Add(Add(16, Mul(15, Pow(2, Div(1, 4)))), Mul(12, Sqrt(2))), Mul(9, Pow(8, Div(1, 4)))), 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