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Mathematics of Computation

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High precision evaluation of the irregular Coulomb wave functions

Authors: A. J. Strecok and J. A. Gregory
Journal: Math. Comp. 26 (1972), 955-961
MSC: Primary 65D20
MathSciNet review: 0314239
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Abstract: This tutorial paper presents practical methods for accurately evaluating irregular Coulomb wave functions. Rational approximations to $ {G_0}(\eta ,\rho )$ and $ {G'_0}(\eta ,\rho )$ are developed along line segments in the $ (\eta ,\rho )$ plane to provide useful initial values for the associated differential equation. These approximations, designed for IBM System 360 Fortran double precision, yield results to at least 13 significant decimal places.

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Keywords: Coulomb wave functions, differential equations, rational approximations
Article copyright: © Copyright 1972 American Mathematical Society