Samiksha Jaiswal (Editor)

Chazy equation

Updated on
Edit
Like
Comment
Share on FacebookTweet on TwitterShare on LinkedInShare on Reddit

In mathematics, the Chazy equation is the differential equation

d 3 y d x 3 = 2 y d 2 y d x 2 − 3 ( d y d x ) 2 .

It was introduced by Jean Chazy (1909, 1911) 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

E 2 ( τ ) = 1 − 24 ∑ σ 1 ( n ) q n = 1 − 24 q − 72 q 2 − ⋯ .

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

References

Chazy equation Wikipedia
(Text) CC BY-SA