Pacific Journal of Mathematics

Elementary solutions of differential equations.

Michael F. Singer

Article information

Source
Pacific J. Math., Volume 59, Number 2 (1975), 535-547.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102905362

Mathematical Reviews number (MathSciNet)
MR0389874

Zentralblatt MATH identifier
0315.12103

Subjects
Primary: 12H05: Differential algebra [See also 13Nxx]

Citation

Singer, Michael F. Elementary solutions of differential equations. Pacific J. Math. 59 (1975), no. 2, 535--547. https://projecteuclid.org/euclid.pjm/1102905362


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References

  • [1] L. Koenigsberger, Bemerkungen zu Liouville's Classificirungder Transcendent en, Math. Ann., 28 (1887), 482-492.
  • [2] D. Mordukhai-Boltovski, Sur la Resolution des Equations Differentielles du Premier Order en form Finie, Rend. Cir. Mat. Palermo, 61 (1937), 49-72.
  • [3] R. Risch, The problem of integrationin finite terms, Trans. Amer. Math. Soc, 139 (1969) 167-189.
  • [4] J. F. Ritt, Integrationin Finite Terms, Columbia University Press, New York, 1948.
  • [5] M. Rosenlicht, Liouville's theorem on functionswith elementary integrals, Pacific J. of Math., 24 (1968), 153-161.
  • [6] M. Rosenlicht, On the explicit solvability of certain transcendental equations, Inst. Haute Etudes Sci. Publ. Math., 36 (1969), 15-22.
  • [7] A. Seidenberg, Some Basic Theorems in DifferentialAlgebra (Characteristic p, arbitrary), Trans. Amer. Math. Soc, 6 (1952), 174-190.
  • [8] M. Singer, Functions SatisfyingElementary Relations, To appear.