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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
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 $ {\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.


References [Enhancements On Off] (What's this?)

  • [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 (35 #3927)
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  • [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, http://dx.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, http://dx.doi.org/10.1007/BF02162028

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1970-0273785-4
PII: S 0025-5718(1970)0273785-4
Keywords: Rational Chebyshev approximations, Coulomb phase shift, complex gamma function
Article copyright: © Copyright 1970 American Mathematical Society