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High precision evaluation of the irregular Coulomb wave functions

1972; American Mathematical Society; Volume: 26; Issue: 120 Linguagem: Inglês

10.1090/s0025-5718-1972-0314239-8

1088-6842

Anthony J. Strecok, John Gregory,

Mathematical functions and polynomials

This tutorial paper presents practical methods for accurately evaluating irregular Coulomb wave functions. Rational approximations to G 0 ( η , ρ ) {G_0}(\eta ,\rho ) and G 0 ′ ( η , ρ ) {G’_0}(\eta ,\rho ) are developed along line segments in the ( η , ρ ) (\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.