Fungrim entry: df5f38

\eta^{2}\!\left(\tau\right) \left(33 {\left(\eta''(\tau)\right)}^{2} + \eta(\tau) {\eta}^{(4)}(\tau)\right) - 18 {\left(\eta'(\tau)\right)}^{4} + 12 \eta(\tau) \eta''(\tau) {\left(\eta'(\tau)\right)}^{2} - 28 \eta^{2}\!\left(\tau\right) \eta'''(\tau) \eta'(\tau) = 0

Assumptions:

\tau \in \mathbb{H}

References:

http://functions.wolfram.com/EllipticFunctions/DedekindEta/13/01/0001/

TeX:

\eta^{2}\!\left(\tau\right) \left(33 {\left(\eta''(\tau)\right)}^{2} + \eta(\tau) {\eta}^{(4)}(\tau)\right) - 18 {\left(\eta'(\tau)\right)}^{4} + 12 \eta(\tau) \eta''(\tau) {\left(\eta'(\tau)\right)}^{2} - 28 \eta^{2}\!\left(\tau\right) \eta'''(\tau) \eta'(\tau) = 0

\tau \in \mathbb{H}

Definitions:

Fungrim symbol	Notation	Short description
`Pow`	${a}^{b}$	Power
`DedekindEta`	$\eta(\tau)$	Dedekind eta function
`ComplexDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("df5f38"),
    Formula(Equal(Sub(Add(Sub(Mul(Pow(DedekindEta(tau), 2), Add(Mul(33, Pow(ComplexDerivative(DedekindEta(tau), For(tau, tau, 2)), 2)), Mul(DedekindEta(tau), ComplexDerivative(DedekindEta(tau), For(tau, tau, 4))))), Mul(18, Pow(ComplexDerivative(DedekindEta(tau), For(tau, tau)), 4))), Mul(Mul(Mul(12, DedekindEta(tau)), ComplexDerivative(DedekindEta(tau), For(tau, tau, 2))), Pow(ComplexDerivative(DedekindEta(tau), For(tau, tau)), 2))), Mul(Mul(Mul(28, Pow(DedekindEta(tau), 2)), ComplexDerivative(DedekindEta(tau), For(tau, tau, 3))), ComplexDerivative(DedekindEta(tau), For(tau, tau)))), 0)),
    Variables(tau),
    Assumptions(Element(tau, HH)),
    References("http://functions.wolfram.com/EllipticFunctions/DedekindEta/13/01/0001/"))

Topics using this entry

Dedekind eta function