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On the numerical calculation of elliptic integrals of the first and second kind and the elliptic functions of Jacobi

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References

  1. King, A. V.: On the direct numerical calculation of Elliptic Functions and Integrals. London: Cambr. Un. Press 1924.

    Google Scholar 

  2. Gauss, C. F.: Nachlaß zur Theorie des arithmetisch-geometrischen Mittels. Herausgeg. vonH. Geppert. Leipzig: Akad. Verlags-Gesellschaft 1927.

    Google Scholar 

  3. Di Donati, A. R., andA. V. Hershey: New Formulas for Computing Incomplete Elliptic Integrals of the First and Second Kind. J. of the A.C.M., Jan. 1959, p. 515.

  4. Jefferson, David K.: ALGORITHM 73 Incomplete Elliptic Integrals. Comm. of the A.C.M., Dec. 1961, p. 543.

  5. Magnus, W., u.F. Oberhettinger: Formeln und Sätze für die speziellen Funktionen der mathematischen Physik. Berlin-Göttingen-Heidelberg: Springer 1948.

    Google Scholar 

  6. Legendre, A. M., u.F. Emde: Tafeln der Elliptischen Normalintegrale erster und zweiter Gattung. Stuttgart: Wittwer 1931.

    Google Scholar 

  7. Ward, Morgan: The Calculation of the Complete Elliptic Integral of the third kind. Ann. Math. Monthly67, 205–213 (1960).

    Google Scholar 

  8. Spenceley, G. W., andR. W.: Smithsonian Elliptic Functions Tables. Smithsonian Institution, Washington 1947.

    Google Scholar 

  9. Salzer, Herbert E.: Quick Calculation of Jacobian Elliptic functions. Comm. of the A.C.M. 1962, p. 399.

  10. Lee-Whiting, G. E.: Formulas for Computing Incomplete Elliptic Integrals of the First and Second Kind. J. of the A.C.M. April 1963, p. 126.

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  1. Mathematisch Centrum, 2e Boerhaavestraat 49, Amsterdam-O

    D. J. Hofsommer & R. P. van de Riet

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  1. D. J. Hofsommer
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  2. R. P. van de Riet
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Report TW 94, Mathematical Centre Amsterdam, November 1962.

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Hofsommer, D.J., van de Riet, R.P. On the numerical calculation of elliptic integrals of the first and second kind and the elliptic functions of Jacobi. Numer. Math. 5, 291–302 (1963). https://doi.org/10.1007/BF01385899

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  • DOI: https://doi.org/10.1007/BF01385899

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