mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, the Chazy equation is the

differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

\frac = 2y\frac - 3 \left(\frac\right)^2.

It was introduced by 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 Eisenstein series, named after German mathematician Gotthold Eisenstein, are particular modular forms with infinite series expansions that may be written down directly. Originally defined for the modular group, Eisenstein series can be generaliz ...

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

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

References

* * * Ordinary differential equations {{mathanalysis-stub