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Rational approximations for the Fresnel integrals


Author: Mark A. Heald
Journal: Math. Comp. 44 (1985), 459-461
MSC: Primary 65D30
DOI: https://doi.org/10.1090/S0025-5718-1985-0777277-6
Corrigendum: Math. Comp. 46 (1986), 771.
Corrigendum: Math. Comp. 46 (1986), 771.
MathSciNet review: 777277
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Abstract | References | Similar Articles | Additional Information

Abstract: A class of simple rational polynomial approximations for the Fresnel integrals is given with maximum errors from $ 1.7 \times {10^{ - 3}}$ down to $ 4 \times {10^{ - 8}}$. The domain $ [0,\infty ]$ is not subdivided. The format is particularly convenient for programmable hand calculators and microcomputer subroutines.


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

  • [1] M. Abramowitz & I. A. Stegun, Editors, Handbook of Mathematical Functions, Dover, New York, 1965. See §§7.3.32-33 and Tables 7.7-8.
  • [2] J. Boersma, "Computation of Fresnel integrals," Math. Comp., v. 14, 1960, p. 380. MR 0121973 (22:12700)
  • [3] W. J. Cody, "Chebyshev approximations for the Fresnel integrals," Math. Comp., v. 22, 1968, pp. 450-453. MR 0238469 (38:6745)
  • [4] C. Hastings, Jr., "Approximations for calculating Fresnel integrals," Math. Comp. [MTAC], v. 10, 1956, p. 173.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1985-0777277-6
Keywords: Rational Chebyshev approximations, Fresnel integrals
Article copyright: © Copyright 1985 American Mathematical Society

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