Coulomb and Bessel functions of complex arguments and order
type: Item
instance of: scholarly article
title: Coulomb and Bessel functions of complex arguments and order
zbMATH Open document ID: 0626.65014
DOI: 10.1016/0021-9991(86)90046-X
author: I. J. Thompson
author: A. Ross Barnett
published in: Journal of Computational Physics
publication date: 1986-01-01T00:00:00Z
review text: The differential equation \(f''(\rho)+(1-2\eta /\rho -\lambda (\lambda +1)/\rho^ 2)f(\rho)=0\) has two linearly independent solutions \(F_{\lambda}(\eta,\rho)\) and \(G_{\lambda}(\eta,\rho)\) called Coulomb wavefunctions. The real functions \(F_{\lambda}\), \(G_{\lambda}\), \((d/d\rho)G_{\lambda}\) and \((d/d\rho)F_{\lambda}\) have been studied extensively and methods of calculations have been developed by several authors. The most important technique has been developed by the second author et al. in 1974, where the authors calculate regular and irregular functions and their derivatives for any real \(\lambda\) or for a range of integer-spaced \(\lambda\)-values. In the present paper the authors define Columb wavefunctions in the complex case and generalize the earlier method to calculate the functions \(F_{\lambda}\), \(G_{\lambda}\), \((d/d\rho)F_{\lambda}\) and \((d/d\rho)G_{\lambda}\) where all variables are complex.
reviewed by: A. Laforgia
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 33E15
Mathematics Subject Classification ID: 33C10
zbMATH DE Number: 4018214
zbMATH Keywords: complex arguments
zbMATH Keywords: continued-fraction expansions
zbMATH Keywords: Bessel functions
zbMATH Keywords: Coulomb wavefunctions
describes a project that uses: COULFG
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4018214