High precision evaluation of the irregular Coulomb wave functions

Strecok, A. J.; Gregory, J. A.

doi:10.1090/S0025-5718-1972-0314239-8

High precision evaluation of the irregular Coulomb wave functions
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by A. J. Strecok and J. A. Gregory PDF

Math. Comp. 26 (1972), 955-961 Request permission

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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