• James H. Davenport
Part of the Lecture Notes in Computer Science book series (LNCS, volume 174)


In this paper, we look closely at the equation of the title, originally considered by Risch, which arises in the integration of exponentials. We present a minor improvement of Risch's original presentation, a generalisation of that presentation to algebraic functions f and g, and a new algorithm for the solution of this equation. Full details of the last two are to appear elsewhere.


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7. References

  1. [Abdali et al., 1977]
    Abdali,S.K., Caviness,B.F. & Pridor.A., Modular Polynomial Arithmetic in Partial Fraction Decomposition. Proc. 1977 MACSYMA Users' Conference (NASA Publ. CP-2012) pp. 253–261.Google Scholar
  2. [Cherry, 1983]
    Cherry,G.W., Algorithms for Integrating Elementary Functions in Terms of Lagarithmic Integrals and Error Functions. Ph.D. Thesis, University of Delaware, August 1983.Google Scholar
  3. [Davenport, 1983]
    Davenport,J.H., The Risch Differential Equation. Manuscript, Aug. 1983. Submitted to SIAM J. Comp.Google Scholar
  4. [Davenport, 1984]
    Davenport,J.H., Integration Algorithmique des fonctions elementairement transcendantes sur une courbe algebrique. To appear in Annales de l'Institut Fourier, 34(1984).Google Scholar
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    Kung, H.T. & Tong, D.M., Fast Algorithms for Partial Fraction Decomposition. SIAM J. Comp. 6(1977) pp. 582–593. MR 58(1979) #13919.Google Scholar
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    Ostrowski, A.M., Sur l'integrabilite elementaire de quelques classes d'expressions. Comm. Math. Helvet. 18(1946) pp. 283–308.Google Scholar
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    Risch, R.H., The Problem of Integration in Finite Terms. Trans. AMS 139(1969) pp. 167–189. MR 38(1969) #5759.Google Scholar
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    Yun,D.Y.Y., Fast Algorithms for Rational Function Integration. Proc. IFIP 1977, North-Holland, 1977, pp. 493–498.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • James H. Davenport
    • 1
  1. 1.School of MathematicsUniversity of BathBathEngland

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