Fuchs's theorem
In mathematics, Fuchs's theorem, named after Lazarus Fuchs, states that a second-order [differential equation] of the form
has a solution expressible by a generalised Frobenius series when, and are analytic at or is a regular singular point. That is, any solution to this second-order differential equation can be written as
for some positive real s, or
for some positive real r, where y0 is a solution of the first kind.
Its radius of convergence is at least as large as the minimum of the radii of convergence of, and.