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Numerical evaluation of the dilogarithm of complex argument

  • Carlos Osácar
  • Jesús Palacián
  • Manuel Palacios
Article

Abstract

A numerical algorithm to evaluate the dilogarithmic function of a complex argument is proposed. The use of the dilogarithm in celestial mechanics appears in the exact Delaunay normalization of some functions involving the equation of the centre.

Key words

special function numerical evaluation convergence acceleration Gaussian quadrature 

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References

  1. 1.
    Abramowitz, M. and Stegun, I. A.: 1985,Handbook of Mathematical Functions, Dover Publications Inc, New York.Google Scholar
  2. 2.
    Burden, R. L. and Faires, J. D.: 1993,Numerical Analysis, PWS-KENT Publishing Company, Boston.Google Scholar
  3. 3.
    Ginsberg, E. S. and Zaborowski, D.: 1973 The Dilogarithm Function of a Real Argument,Collected Algorithms from CACM 490, 1–0.Google Scholar
  4. 4.
    Lewin, L.: 1958,Dilogarithms and Associated Functions, Macdonald Ed., London.Google Scholar
  5. 5.
    Osácar, C. and Palacián, J.: 1994,Celes. Mech & Dynam. Astron. 60, 207.Google Scholar
  6. 6.
    Rall, K. and Jones, L.: 1992,Language Systems, FORTRAN 3.0, Reference Manual, Language Systems Corporation, Herndon, VA.Google Scholar
  7. 7.
    Van Wijngaarden, A.: 1954,Polylogarithms, by the Staff of the Computation Department, Report R. 24, Part I, Numerical Values, Mathematisch Centrum, Amsterdam, Holland.Google Scholar
  8. 8.
    Wolfram, S.: 1991,Mathematica. A System for Doing Mathematics by Computer, Second edition. Addison-Wesley Publishing Company, Inc., Redwood City, CA.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Carlos Osácar
    • 1
  • Jesús Palacián
    • 1
  • Manuel Palacios
    • 1
  1. 1.Grupo de Mecánica Espacial Universidad de ZaragozaZaragozaSpain

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