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Fungrim entry: df5f38

η2 ⁣(τ)(33(η(τ))2+η(τ)η(4)(τ))18(η(τ))4+12η(τ)η(τ)(η(τ))228η2 ⁣(τ)η(τ)η(τ)=0\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:τH\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
Powab{a}^{b} Power
DedekindEtaη(τ)\eta(\tau) Dedekind eta function
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
HHH\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/"))

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2019-10-05 13:11:19.856591 UTC