Английская Википедия:Chazy equation

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In mathematics, the Chazy equation is the differential equation

<math> \frac{d^3y}{dx^3} = 2y\frac{d^2y}{dx^2} - 3 \left(\frac{dy}{dx}\right)^2.</math>

It was introduced by Шаблон:Harvs as an example of a third-order differential equation with a movable singularity that is a natural boundary for its solutions.

One solution is given by the Eisenstein series

<math>E_2(\tau) =1-24\sum \sigma_1(n)q^n= 1-24q-72q^2-\cdots.</math>

Acting on this solution by the group SL2 gives a 3-parameter family of solutions.

References


Шаблон:Mathanalysis-stub