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COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments. (English) Zbl 0578.65016
Summary: The routine COULCC calculates both the oscillating and the exponentially varying Coulomb wave functions, and their radial derivatives, for complex $\eta$ (Sommerfeld parameter), complex energies and complex angular momenta. The functions for uncharged scattering (spherical Bessels) and cylindrical Bessel functions are special cases which are more easily solved. Two linearly independent solutions are found, in general, to the differential equation $f''(x)+g(x)f(x)=0$, where g(x) has $x\sp 0$, $x\sp{-1}$ and $x\sp{-2}$ terms, with coefficients 1, -2$\eta$ and $- \lambda (\lambda +1)$, respectively.

65D20Computation of special functions, construction of tables
33C55Spherical harmonics
33E10Lamé, Mathieu, and spheroidal wave functions
Full Text: DOI
[1] Barnett, A. R.; Feng, D. H.; Steed, J. W.; Goldfarb, L. J. B.: Comput. phys. Commun.. 8, 377 (1974)
[2] Barnett, A. R.: Comput. phys. Commun.. 24, 141 (1981)
[3] Barnett, A. R.: J. comput. Phys.. 46, 171 (1982)
[4] Barnett, A. R.: Comput. phys. Commun.. 21, 297 (1981)
[5] Barnett, A. R.: J. comput. Appl. math.. 8, 29 (1982)
[6] Feng, D. H.; Barnett, A. R.; Goldfarb, L. J. B.: Phys. rev.. 13C, 1151 (1976)
[7] Barnett, A. R.: Comput. phys. Commun.. 27, 147 (1982)
[8] Seaton, M. J.: Comput. phys. Commun.. 25, 87 (1982)
[9] Tamura, T.; Rybicki, F.: Comput. phys. Commun.. 1, 25 (1969)
[10] Takemasa, T.; Tamura, T.; Wolter, H. H.: Comput. phys. Commun.. 17, 351 (1979)
[11] Bell, K. L.; Scott, N. S.: Comput. phys. Commun.. 20, 447 (1980)
[12] Hebbard, D. F.; Robson, B. A.: Nucl. phys.. 42, 563 (1963)
[13] Curtis, A. R.: Coulomb wave functions, vol. 11, royal soc. Math. tables. 11, 9 (1964) · Zbl 0122.36204
[14] . Ann. phys. 155, 461 (1984)
[15] Noble, C. J.; Thompson, I. J.: Comput. phys. Commun.. 33, 413 (1984)
[16] I.J. Thompson and A.R. Barnett, J. Comput. Phys. (submitted).
[17] . NBS applied math. Ser. 17 (1952)
[18] Patry, J.; Gupta, S.: EIR-bericht nr. 247. (1973)
[19] Kölbig, K. S.: Comput. phys. Commun.. 4, 221 (1972)