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

Dedekind eta function