Fungrim entry: 0701dc

\eta\!\left(16 i\right) = \frac{1}{{2}^{113 / 64}} \frac{{\left({2}^{1 / 4} - 1\right)}^{1 / 4}}{{\left(1 + \sqrt{2}\right)}^{1 / 16}} {\left(-{2}^{5 / 8} + \sqrt{1 + \sqrt{2}}\right)}^{1 / 2} \eta(i)

References:

https://math.stackexchange.com/questions/1334684/what-is-the-exact-value-of-eta6i/1334940

TeX:

\eta\!\left(16 i\right) = \frac{1}{{2}^{113 / 64}} \frac{{\left({2}^{1 / 4} - 1\right)}^{1 / 4}}{{\left(1 + \sqrt{2}\right)}^{1 / 16}} {\left(-{2}^{5 / 8} + \sqrt{1 + \sqrt{2}}\right)}^{1 / 2} \eta(i)

Definitions:

Fungrim symbol	Notation	Short description
`DedekindEta`	$\eta(\tau)$	Dedekind eta function
`ConstI`	$i$	Imaginary unit
`Pow`	${a}^{b}$	Power
`Sqrt`	$\sqrt{z}$	Principal square root

Source code for this entry:

Entry(ID("0701dc"),
    Formula(Equal(DedekindEta(Mul(16, ConstI)), Mul(Mul(Mul(Div(1, Pow(2, Div(113, 64))), Div(Pow(Sub(Pow(2, Div(1, 4)), 1), Div(1, 4)), Pow(Add(1, Sqrt(2)), Div(1, 16)))), Pow(Add(Neg(Pow(2, Div(5, 8))), Sqrt(Add(1, Sqrt(2)))), Div(1, 2))), DedekindEta(ConstI)))),
    References("https://math.stackexchange.com/questions/1334684/what-is-the-exact-value-of-eta6i/1334940"))

Topics using this entry

Dedekind eta function