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Fungrim entry: 02d14f

36(y(τ))224y(τ)y ⁣(τ)+y(τ)=0   where y ⁣(τ)=η(τ)η ⁣(τ)36 {\left(y'(\tau)\right)}^{2} - 24 y''(\tau) y\!\left(\tau\right) + y'''(\tau) = 0\; \text{ where } y\!\left(\tau\right) = \frac{\eta'(\tau)}{\eta\!\left(\tau\right)}
Assumptions:τH\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\!\left(\tau\right) + y'''(\tau) = 0\; \text{ where } y\!\left(\tau\right) = \frac{\eta'(\tau)}{\eta\!\left(\tau\right)}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
DedekindEtaη ⁣(τ)\eta\!\left(\tau\right) Dedekind eta function
HHH\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), tau, tau), 2)), Mul(Mul(24, ComplexDerivative(y(tau), tau, tau, 2)), y(tau))), ComplexDerivative(y(tau), tau, tau, 3)), 0), Equal(y(tau), Div(ComplexDerivative(DedekindEta(tau), tau, tau), DedekindEta(tau))))),
    Variables(tau),
    Assumptions(Element(tau, HH)),
    References("http://functions.wolfram.com/EllipticFunctions/DedekindEta/13/01/0002/"))

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2019-08-19 14:38:23.809000 UTC