Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Chebyshev approximations for the Coulomb phase shift
HTML articles powered by AMS MathViewer

by W. J. Cody and K. E. Hillstrom PDF
Math. Comp. 24 (1970), 671-677 Request permission


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.
    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 three-term recurrence relations, SIAM Rev. 9 (1967), 24–82. MR 213062, DOI 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 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 10.1007/BF02162028
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 65.25
  • Retrieve articles in all journals with MSC: 65.25
Additional Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Math. Comp. 24 (1970), 671-677
  • MSC: Primary 65.25
  • DOI:
  • MathSciNet review: 0273785