Fuchs' theorem

In mathematics, Fuchs' 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 .