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Mathematische Annalen

, Volume 74, Issue 1, pp 134–139 | Cite as

Equivalent singular points of ordinary linear differential equations

  • George D. Birkhoff
Article

Keywords

Differential Equation Singular Point Linear Differential Equation Ordinary Linear Differential Equation 
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References

  1. Trans. Am. Math. Soc. 10, p. 436–470.Google Scholar
  2. Loc. cit. Trans. Am. Math. Soc. 10 p. 446 and p. 453.Google Scholar
  3. For these definitions see Schlesinger,Vorlesungen über lineare Differentialgleichungen, p. 181.Google Scholar
  4. For an exposition of the elementary properties of matrices used in the present paper see Schlesinger, loc. cit.,Vorlesungen über lineare Differentialgleichungen, p. 18–19.Google Scholar
  5. This definition is more satisfactory than the one used in my earlier paper (Trans. Am. Math. Soc., loc. cit. 10 p. 446 and p. 453.) where the functionsa ij (x) were merely restricted to be rational in character atx=∞.Google Scholar
  6. For a complete discussion of the facts outlined here see Schlesinger, loc. cit.,Vorlesungen über lineare Differentialgleichungen, p. 90–104.Google Scholar
  7. Schlesinger, loc. cit.,Vorlesungen über lineare Differentialgleichungen, p. 21.Google Scholar

Copyright information

© Springer-Verlag 1913

Authors and Affiliations

  • George D. Birkhoff
    • 1
  1. 1.CambridgeUSA

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