Fungrim entry: 7cc3d3

\eta\!\left(7 i\right) = \frac{1}{\sqrt{7}} {\left(-\frac{7}{2} + \sqrt{7} + \frac{1}{2} \sqrt{-7 + 4 \sqrt{7}}\right)}^{1 / 4} \eta(i)

References:

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

TeX:

\eta\!\left(7 i\right) = \frac{1}{\sqrt{7}} {\left(-\frac{7}{2} + \sqrt{7} + \frac{1}{2} \sqrt{-7 + 4 \sqrt{7}}\right)}^{1 / 4} \eta(i)

Definitions:

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

Source code for this entry:

Entry(ID("7cc3d3"),
    Formula(Equal(DedekindEta(Mul(7, ConstI)), Mul(Mul(Div(1, Sqrt(7)), Pow(Add(Add(Neg(Div(7, 2)), Sqrt(7)), Mul(Div(1, 2), Sqrt(Add(-7, Mul(4, Sqrt(7)))))), Div(1, 4))), DedekindEta(ConstI)))),
    References("https://math.stackexchange.com/questions/1334684/what-is-the-exact-value-of-eta6i/1334940"))

Topics using this entry

Dedekind eta function

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC