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]**M. Abramowitz & I. A. Stegun (Editors),*Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables*, National Bureau of Standards Appl. Math. Series, No. 55, U. S. Government Printing Office, Washington, D. C., 1964. MR**31**#1400. MR**0167642 (29:4914)****[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 (Unpublished.)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.*, v. 14, 1960, p. 380. MR**22**#12700. MR**0121973 (22:12700)****[4]**G. Németh, "Chebyshev expansions for Fresnel integrals,"*Numer. Math.*, v. 7, 1965, pp. 310-312. MR**32**#3265. MR**0185805 (32:3265)****[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]**P. Henrici, "The quotient-difference algorithm,"*Nat. Bur. Standards Appl. Math. Ser.*, no. 49, 1958, pp. 23-46. MR**20**#1410. MR**0094901 (20:1410)****[8]**J. R. Rick, "On the conditioning of polynomial and rational forms,"*Numer. Math.*, v. 7, 1965, pp. 426-435. MR**32**#6710. MR**0189283 (32:6710)**

Additional Information

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

Article copyright:
© Copyright 1968
American Mathematical Society