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
Corrigendum:
Math. Comp. 26 (1972), 1031.
MathSciNet review:
0273785
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Abstract 
References 
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Abstract: This note presents nearlybest 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. 537554. MR 29 #4914.
 [2]
Walter
Gautschi, Computational aspects of threeterm recurrence
relations, SIAM Rev. 9 (1967), 24–82. MR 0213062
(35 #3927)
 [3]
W. Gautschi, "Algorithm 292, regular Coulomb wave functions," Comm. ACM, v. 9, 1966, pp. 793795.
 [4]
H. F. Lutz & M. D. Karvelis, "Numerical calculation of Coulomb wave functions for repulsive Coulomb fields," Nuclear Phys., v. 43, 1963, pp. 3144.
 [5]
J. H. Gunn, "Algorithm 300, Coulomb wave functions," Comm. ACM, v. 10, 1967, pp. 244245.
 [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
 [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. 537554. MR 29 #4914.
 [2]
 W. Gautschi, "Computational aspects of threeterm recurrence relations," SIAM Rev., v. 9, 1967, pp. 2482. MR 35 #3927. MR 0213062 (35:3927)
 [3]
 W. Gautschi, "Algorithm 292, regular Coulomb wave functions," Comm. ACM, v. 9, 1966, pp. 793795.
 [4]
 H. F. Lutz & M. D. Karvelis, "Numerical calculation of Coulomb wave functions for repulsive Coulomb fields," Nuclear Phys., v. 43, 1963, pp. 3144.
 [5]
 J. H. Gunn, "Algorithm 300, Coulomb wave functions," Comm. ACM, v. 10, 1967, pp. 244245.
 [6]
 W. J. Cody, W. Fraser & J. F. Hart, "Rational Chebyshev approximation using linear equations," Numer. Math., v. 12, 1968, pp. 242251. MR 1553964
 [7]
 H. Werner, J. Stoer & W. Bommas, "Rational Chebyshev approximation," Numer. Math., v. 10, 1967, pp. 289306. MR 1553955
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197002737854
PII:
S 00255718(1970)02737854
Keywords:
Rational Chebyshev approximations,
Coulomb phase shift,
complex gamma function
Article copyright:
© Copyright 1970
American Mathematical Society
