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Numerische Mathematik

, Volume 13, Issue 3, pp 266–284 | Cite as

An extension of the Bartky-transformation to incomplete elliptic integrals of the third kind

  • R. Bulirsch
Article

Keywords

Mathematical Method Elliptic Integral Incomplete Elliptic Integral 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Abramowitz, M., andI. A. Stegun: Handbook of mathematical functions. New York: Dover (1965)Google Scholar
  2. 2.
    Alway, G. G.: Multhopp's influence functions and their automatic computation. Quart. J. Mech.13, 192–918 (1960).Google Scholar
  3. 3.
    Bartky, W.: Numerical calculation of a generalized complete elliptic integral. Rev. Mod. Phys.10, 264–269 (1938).Google Scholar
  4. 4.
    Bulirsch, R.: Numerical calculation of elliptic integrals and elliptic functions I, II. Numer. Math.7, 78–90, 353–354 (1965).Google Scholar
  5. 5.
    ——, u.J. Stoer: Darstellung von Funktionen in Rechenautomaten. Contrib. to „Mathematische Hilfsmittel des Ingenieurs III”, Editors:R. Sauer, I. Szábo. Berlin-Heidelberg-New York: Springer 1968.Google Scholar
  6. 6.
    — Numerical calculation of elliptic integrals and elliptic functions III. To appear in Numer. Math.Google Scholar
  7. 7.
    Byrd, P. F., andM. D. Friedman: Handbook of elliptic integrals for engineers and physicists. Berlin-Göttingen-Heidelberg: Springer 1954.Google Scholar
  8. 8.
    Curtis, A. R.: N. P. L. Math. Tables, Vol. 7: Tables of Jacobian elliptic functions whose arguments are rational fractions of the quarter period. London: Her Majesty's Stationary Office 1964.Google Scholar
  9. 9.
    Hofsommer, D. J., andR. P. van de Riet: On the numerical calculation of elliptic integrals of the first and second kind and the elliptic functions of Jacobi. Num. Math.5, 291–302 (1963)Google Scholar
  10. 10.
    Jahnke-Emde-Lösch: Tafeln höherer Funktionen; Tables of higher functions. Stuttgart: Teubner; New York: McGraw-Hill 1960.Google Scholar
  11. 11.
    King, A. V.: On the direct numerical calculation of elliptic functions and integrals. London: Cambr. Un. Press 1924.Google Scholar
  12. 12.
    Tölke, F.: Praktische Funktionenlehre II, III. Berlin-Heidelberg-New York: Springer 1966.Google Scholar
  13. 13.
    Fettis, H. E.: Calculation of elliptic integrals of the third kind by means of Gauss' transformation. Math. Comp.19, 97–104 (1965).Google Scholar

Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • R. Bulirsch
    • 1
  1. 1.Mathematisches Institut der Universität KölnWeyertal 86

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