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Zbl 0578.65016
Thompson, I.J.; Barnett, A.R.
COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments. (English)
[J] Comput. Phys. Commun. 36, 363-372 (1985); erratum ibid. 159, No. 3, 241-242 (2004). ISSN 0010-4655

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.

MSC 2000:: *65D20 Computation of special functions
33C55 Elliptic integrals as hypergeometric functions
33E10 Spheroidal wave functions, etc.

Keywords: Whittaker; hypergeometric; continued fraction; scattering; closed; channels; off-shell; resonances; reactions; Regge poles; Coulomb wave functions; radial derivatives; spherical Bessels; cylindrical Bessel

Cited in: Zbl 1196.65044

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