Numerische Mathematik

, Volume 29, Issue 2, pp 233–236 | Cite as

Calculation of the complete elliptic integrals with complex modulus

  • Tohru Morita
Article

Summary

This is an Addendum to a preceding paper of Morita and Horiguchi [Numer. Math.20, 425–430 (1973)]. Attention is called to an error in the algol procedure given in that paper. A corrected procedure of calculating the complete elliptic integrals of the first and the second kind with complex modulusk is presented, in the form that is itself useful in the calculation of their analytic continuations over the branch cuts.

Subject Classifications

AMS(MOS): 65D20 CR. 5. 12 

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References

  1. 1.
    Bulirsch, R.: Handbook series special functions, numerical calculations of elliptic integrals and elliptic functions. Numer. Math.7, 78–90 (1965)Google Scholar
  2. 2.
    Morita, T., Horiguchi, T.: Calculation of the lattice Green's function of the b.c.c., f.c.c., and rectangular lattices. J. Math. Phys.12, 986–992 (1971)Google Scholar
  3. 3.
    Morita, T., Horiguchi, T.: Table of the lattice Green's function for the cubic lattices (values at the origin). Applied Math. Res. Group, Dept. Applied Science, Fac. Engineering, Tohoku Univ., Sendai, Japan, 1971Google Scholar
  4. 4.
    Morita, T., Horiguchi, T.: Convergence of the arithmetic-geometric mean procedure for the complex variables and the calculation of the complete elliptic integrals with complex modulus. Numer. Math.20, 425–430 (1973)Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Tohru Morita
    • 1
  1. 1.Department of Applied Science, Faculty of EngineeringTohoku UniversitySendaiJapan

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