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Numerical calculation of elliptic integrals and elliptic functions. III

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Summary

This paper is a continuation of [2, 3]. It contains anALGOL program for the incomplete elliptic integral of the third kind based on a theory described in [4]. This program replaces the inadequate one based on the Gauß-transformation which was published in [2]. In addition, anAlgol program for a general complete elliptic integral is presented.

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References

  1. 1.

    Belyakov, V. M., P. I. Kravtsova, andM. G. Rappoport: Tables of elliptic integrals, part I. New York: MacMillan 1965

  2. 2.

    Bulirsch, R.: Numerical calculation of elliptic integrals and elliptic functions. Numer. Math.7, 78–90 (1965).

  3. 3.

    —— Numer. Math.7, 353–354 (1965).

  4. 4.

    ——: An extension of the Bartky-transformation to incomplete elliptic integrals of the third kind. Numer. Math.13, 266–284 (1969)

  5. 5.

    Byrd, P. F., andM. D. Friedman: Handbook of elliptic integrals for engineers and physicists. Berlin-Göttingen-Heidelberg: Springer 1954.

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    Clenshaw, C. W.: Chebyshev series for mathematical functions. London: Her Majesty's Stationary Office 1962.

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    ——,G. F. Miller, andM. Woodger: Algorithms for special functions. I. Numer. Math.4, 403–419 (1963)

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Additional information

Editor's note. In this fascicle, prepublication of algorithms from the Special Functions Series of the Handbook for Automatic Computation is continued. Algorithms are published inAlgol 60 reference language as approved by the IFIP. Contributions in this series should be styled after the most recently published ones.

This research was supported by the Advanced Research Projects Agency of the Department of Defense and was monitored by the U. S. Army Research Office —Durham under Contract DA-31-124-ARO-D-257.

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Bulirsch, R. Numerical calculation of elliptic integrals and elliptic functions. III. Numer. Math. 13, 305–315 (1969). https://doi.org/10.1007/BF02165405

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Keywords

  • Numerical Calculation
  • Mathematical Method
  • Elliptic Function
  • Elliptic Integral