Skip to main content
Log in

Numerical calculation of elliptic integrals and elliptic functions

  • Handbook Series Special Functions
  • Published:
Numerische Mathematik Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Clenshaw, C. W., G. F. Miller, andM. Woodger: Handbook Series Special Functions, Algorithms for Special Functions I. Num. Math.4, 403–419 (1963).

    Google Scholar 

  2. Bartky, W.: Numerical Calculation of a Generalized Complete Elliptic Integral. Rev. Mod. Phys.10, 264–269 (1938)

    Google Scholar 

  3. Alway, G. G.: Multhopp's Influence Functions and their Automatic Computation. Quart. J. Mech.13, 112–118 (1960).

    Google Scholar 

  4. 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 

  5. Index by Subject to Algorithms, S 21. Communications of the ACM7, 146–148 (1964).

    Google Scholar 

  6. Jahnke-Emde-Lösch: Tafeln höherer Funktionen, Tables of Higher Functions. Stuttgart: B. G. Teubner; New York: McGraw-Hill Book Comp., Inc. 1960.

    Google Scholar 

  7. Byrd, P. F., andM. D. Friedman: Handbook of Elliptic Integrals for Engineers and Physicists. Berlin-Göttingen-Heidelberg: Springer 1954.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  10. 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 Stationery Office 1964.

    Google Scholar 

  11. Lee-Whiting, G. E.: Formulas for Computing Incomplete Elliptic Integrals of the First and Second Kind. J. of the A.C.M.10, 126–130 (1963).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Editor's note. In this fascicle, prepublication of algorithms from the Special Function 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.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bulirsch, R. Numerical calculation of elliptic integrals and elliptic functions. Numer. Math. 7, 78–90 (1965). https://doi.org/10.1007/BF01397975

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01397975

Keywords

Navigation