Chebyshev approximations for the Coulomb phase shift

Authors:
W. J. Cody and K. E. Hillstrom

Journal:
Math. Comp. **24** (1970), 671-677

MSC:
Primary 65.25

DOI:
https://doi.org/10.1090/S0025-5718-1970-0273785-4

Corrigendum:
Math. Comp. **26** (1972), 1031.

MathSciNet review:
0273785

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Abstract | References | Similar Articles | Additional Information

Abstract: This note presents nearly-best rational approximations for the Coulomb phase shift . Maximal relative errors range down to between and . The nontrivial zero of is also given.

**[1]**M. Abramowitz, "Coulomb wave functions,"*Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables*, M. Abramowitz & I. A. Stegun (Editors), Nat. Bur. Standards Appl. Math. Series, 55, Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964, chap. 14, pp. 537-554. MR**29**#4914.**[2]**Walter Gautschi,*Computational aspects of three-term recurrence relations*, SIAM Rev.**9**(1967), 24–82. MR**0213062**, https://doi.org/10.1137/1009002**[3]**W. Gautschi, "Algorithm 292, regular Coulomb wave functions,"*Comm. ACM*, v. 9, 1966, pp. 793-795.**[4]**H. F. Lutz & M. D. Karvelis, "Numerical calculation of Coulomb wave functions for repulsive Coulomb fields,"*Nuclear Phys.*, v. 43, 1963, pp. 31-44.**[5]**J. H. Gunn, "Algorithm 300, Coulomb wave functions,"*Comm. ACM*, v. 10, 1967, pp. 244-245.**[6]**W. J. Cody,*Handbook Series Methods of Approximation: Rational Chebyshev approximation using linear equations*, Numer. Math.**12**(1968), no. 4, 242–251. MR**1553964**, https://doi.org/10.1007/BF02162506**[7]**H. Werner, J. Stoer, and W. Bommas,*Handbook Series Methods of Approximation: Rational Chebyshev approximation*, Numer. Math.**10**(1967), no. 4, 289–306. MR**1553955**, https://doi.org/10.1007/BF02162028

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1970-0273785-4

Keywords:
Rational Chebyshev approximations,
Coulomb phase shift,
complex gamma function

Article copyright:
© Copyright 1970
American Mathematical Society