Fuchs' theorem

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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 .

See also[edit]


  • 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 .