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.
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References
Bulirsch, R.: Handbook series special functions, numerical calculations of elliptic integrals and elliptic functions. Numer. Math.7, 78–90 (1965)
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)
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, 1971
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)
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Morita, T. Calculation of the complete elliptic integrals with complex modulus. Numer. Math. 29, 233–236 (1978). https://doi.org/10.1007/BF01390341
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DOI: https://doi.org/10.1007/BF01390341