Chebyshev approximations for the Fresnel integrals

Author:
W. J. Cody

Journal:
Math. Comp. **22** (1968), 450-453

DOI:
https://doi.org/10.1090/S0025-5718-68-99871-2

MathSciNet review:
0238469

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Abstract | References | Additional Information

Abstract: Rational Chebyshev approimations have been computed for the Fresnel integrals and for arguments in the intervals and , and for the related functions and for the intervals , and . Maximal relative errors range down to .

**[1]**Milton Abramowitz and Irene A. Stegun,*Handbook of mathematical functions with formulas, graphs, and mathematical tables*, National Bureau of Standards Applied Mathematics Series, vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964. MR**0167642****[2]**H. E. Syrett & M. W. Wilson,*Computation of Fresnel Integrals to 28 Figures: Approximations to 8 and 20 Figures*, Univ. of Western Ontario, Canada. (Unpublished.) See*Math. Comp.*, v. 20, 1966, p. 181, RMT**25**.**[3]**J. Boersma,*Computation of Fresnel integrals*, Math. Comp.**14**(1960), 380. MR**0121973**, https://doi.org/10.1090/S0025-5718-1960-0121973-3**[4]**G. Németh,*Chebyshev expansions for Fresnel integrals*, Numer. Math.**7**(1965), 310–312. MR**0185805**, https://doi.org/10.1007/BF01436524**[5]**W. Fraser & J. F. Hart, "On the computation of rational approximations to continuous functions,"*Comm. ACM*, v. 5, 1962, pp. 401-403.**[6]**W. J. Cody & J. Stoer, "Rational Chebyshev approximations using interpolation,"*Numer. Math.*, v. 9, 1966, pp. 177-188.**[7]**Peter Henrici,*The quotient-difference algorithm*, Nat. Bur. Standards Appl. Math. Ser. no.**49**(1958), 23–46. MR**0094901****[8]**John R. Rice,*On the conditioning of polynomial and rational forms*, Numer. Math.**7**(1965), 426–435. MR**0189283**, https://doi.org/10.1007/BF01436257

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-68-99871-2

Article copyright:
© Copyright 1968
American Mathematical Society