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Fuchs' theorem

From Wikipedia, the free encyclopedia

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 .

See also

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References

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  • 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.