# Fungrim entry: 02d14f

$36 {\left(y'(\tau)\right)}^{2} - 24 y''(\tau) y(\tau) + y'''(\tau) = 0\; \text{ where } y(\tau) = \frac{\eta'(\tau)}{\eta(\tau)}$
Assumptions:$\tau \in \mathbb{H}$
References:
• http://functions.wolfram.com/EllipticFunctions/DedekindEta/13/01/0002/
TeX:
36 {\left(y'(\tau)\right)}^{2} - 24 y''(\tau) y(\tau) + y'''(\tau) = 0\; \text{ where } y(\tau) = \frac{\eta'(\tau)}{\eta(\tau)}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
Pow${a}^{b}$ Power
ComplexDerivative$\frac{d}{d z}\, f\!\left(z\right)$ Complex derivative
DedekindEta$\eta(\tau)$ Dedekind eta function
HH$\mathbb{H}$ Upper complex half-plane
Source code for this entry:
Entry(ID("02d14f"),
Formula(Where(Equal(Add(Sub(Mul(36, Pow(ComplexDerivative(y(tau), For(tau, tau)), 2)), Mul(Mul(24, ComplexDerivative(y(tau), For(tau, tau, 2))), y(tau))), ComplexDerivative(y(tau), For(tau, tau, 3))), 0), Equal(y(tau), Div(ComplexDerivative(DedekindEta(tau), For(tau, tau)), DedekindEta(tau))))),
Variables(tau),
Assumptions(Element(tau, HH)),
References("http://functions.wolfram.com/EllipticFunctions/DedekindEta/13/01/0002/"))

## Topics using this entry

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