Numerical Algorithms

, Volume 10, Issue 1, pp 13–26 | Cite as

Numerical computation of real or complex elliptic integrals

  • B. C. Carlson
Article

Abstract

Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind). Numerical check values, consistency checks, and relations to Legendre's integrals and Bulirsch's integrals are included.

Keywords

Elliptic integral algorithm numerical computation 

AMS subject classification

primary 33A25, 33-04, 65D20 secondary 33A10, 30-04, 32-04 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. Bulirsch, Numerical calculation of elliptic integrals and functions, Numer. Math. 7 (1965) 78–90, 353–354; 13 (1969) 305–315.Google Scholar
  2. [2]
    P.F. Byrd and M.D. Friedman,Handbook of Elliptic Integrals for Engineers and Scientists, 2nd ed. (Springer, New York, 1971).Google Scholar
  3. [3]
    B.C. Carlson, On computing elliptic integrals and functions., J. Math. and Phys. 44 (1965) 36–51.Google Scholar
  4. [4]
    B.C. Carlson, Elliptic integrals of the first kind, SIAM J. Math. Anal. 8 (1977) 231–242.Google Scholar
  5. [5]
    B.C. Carlson, Computing elliptic integrals by duplication, Numer. Math. 33 (1979) 1–16.Google Scholar
  6. [6]
    B.C. Carlson and E.M. Notis, Algorithm 577: Algorithms for incomplete elliptic integrals, ACM Trans. Math. Software 7 (1981) 398–403.Google Scholar
  7. [7]
    B.C. Carlson, A table of elliptic integrals of the second kind, Math. Comp. 49 (1987) 595–606. (Supplement, ibid. Math. Comp. 49 (1987) S13–S17.)Google Scholar
  8. [8]
    B.C. Carlson, A table of elliptic integrals of the third kind, Math. Comp. 51 (1988) 267–280. (Supplement, ibid. Math. Comp. 51 (1988) S1–S5.)Google Scholar
  9. [9]
    B.C. Carlson, A table of elliptic integrals: cubic cases, Math. Comp. 53 (1989) 327–333.Google Scholar
  10. [10]
    B.C. Carlson, A table of elliptic integrals: one quadratic factor, Math. Comp. 56 (1991) 267–280.Google Scholar
  11. [11]
    B.C. Carlson, A table of elliptic integrals: two quadratic factors, Math. Comp. 59 (1992) 165–180.Google Scholar
  12. [12]
    G. Fubini, Nuovo metodo per lo studio e per il calcolo delle funzioni transcendenti elementari, Period. Mat. 12 (1897) 169–178.Google Scholar
  13. [13]
    W.H. Press and S.A. Teukolsky, Elliptic integrals, Comp. Phys. 4 (1990) 92–98.Google Scholar
  14. [14]
    W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery,Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed. (Cambridge Univ. Press, New York, 1992).Google Scholar
  15. [15]
    W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery,Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge Univ. Press, New York, 1992).Google Scholar
  16. [16]
    D.G. Zill and B.C. Carlson, Symmetric elliptic integrals of the third kind, Math. Comp. 24 (1970) 199–214.Google Scholar

Copyright information

© J.C. Baltzer AG, Science Publishers 1995

Authors and Affiliations

  • B. C. Carlson
    • 1
  1. 1.Ames Laboratory and Department of MathematicsIowa State UniversityAmesUSA

Personalised recommendations