Chebyshev approximations for the Coulomb phase shift
Authors:
W. J. Cody and K. E. Hillstrom
Journal:
Math. Comp. 24 (1970), 671677
MSC:
Primary 65.25
DOI:
https://doi.org/10.1090/S00255718197002737854
Corrigendum:
Math. Comp. 26 (1972), 1031.
MathSciNet review:
0273785
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Abstract  References  Similar Articles  Additional Information
Abstract: This note presents nearlybest rational approximations for the Coulomb phase shift ${\sigma _0}(\eta ) = \arg \Gamma (1 + i\eta )$. Maximal relative errors range down to between $4.24 \times {10^{  19}}$ and $1.09 \times {10^{  20}}$. The nontrivial zero of ${\sigma _0}(\eta )$ is also given.

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.
 Walter Gautschi, Computational aspects of threeterm recurrence relations, SIAM Rev. 9 (1967), 24–82. MR 213062, DOI https://doi.org/10.1137/1009002 W. Gautschi, "Algorithm 292, regular Coulomb wave functions," Comm. ACM, v. 9, 1966, pp. 793–795. H. F. Lutz & M. D. Karvelis, "Numerical calculation of Coulomb wave functions for repulsive Coulomb fields," Nuclear Phys., v. 43, 1963, pp. 31–44. J. H. Gunn, "Algorithm 300, Coulomb wave functions," Comm. ACM, v. 10, 1967, pp. 244–245.
 W. J. Cody, Handbook Series Methods of Approximation: Rational Chebyshev approximation using linear equations, Numer. Math. 12 (1968), no. 4, 242–251. MR 1553964, DOI https://doi.org/10.1007/BF02162506
 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, DOI https://doi.org/10.1007/BF02162028
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Additional Information
Keywords:
Rational Chebyshev approximations,
Coulomb phase shift,
complex gamma function
Article copyright:
© Copyright 1970
American Mathematical Society