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COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments. (English) Zbl 0578.65016

Comput. Phys. Commun. 36, 363-372 (1985); erratum ibid. 159, No. 3, 241-242 (2004).
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 \(x^ 0\), \(x^{-1}\) and \(x^{-2}\) terms, with coefficients 1, -2\(\eta\) and \(- \lambda (\lambda +1)\), respectively.

MSC:

65D20 Computation of special functions and constants, construction of tables
33C55 Spherical harmonics
33E10 Lamé, Mathieu, and spheroidal wave functions

Software:

COULCC; COULFG
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Full Text: DOI

References:

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