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 real s, or
for some 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 .
- Asmar, Nakhlé H. (2005), Partial differential equations with Fourier series and boundary value problems, Upper Saddle River, NJ: Pearson Prentice Hall, ISBN 0-13-148096-0.
- Butkov, Eugene (1995), Mathematical Physics, Reading, MA: Addison-Wesley, ISBN 0-201-00727-4.