Chebyshev approximations for the Coulomb phase shift
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- by W. J. Cody and K. E. Hillstrom PDF
- Math. Comp. 24 (1970), 671-677 Request permission
Corrigendum: Math. Comp. 26 (1972), 1031.
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
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- 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.
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Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Math. Comp. 24 (1970), 671-677
- MSC: Primary 65.25
- DOI: https://doi.org/10.1090/S0025-5718-1970-0273785-4
- MathSciNet review: 0273785