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 .

See also Frobenius method

References . .