Chebyshev approximations for Dawson's integral

Authors:
W. J. Cody, Kathleen A. Paciorek and Henry C. Thacher

Journal:
Math. Comp. **24** (1970), 171-178

MSC:
Primary 65.20

DOI:
https://doi.org/10.1090/S0025-5718-1970-0258236-8

MathSciNet review:
0258236

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Abstract | References | Similar Articles | Additional Information

Abstract: Rational Chebyshev approximations to Dawson's integral are presented in well-conditioned forms for and . Maximal relative errors range down to between and .

**[1]**W. Gautschi, "Error function and Fresnel integrals," Chapter 7 in*Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables*, M. Abramowitz and I. A. Stegun (Editors), Nat. Bur. Standards Appl. Math. Series, 55, Superintendent of Documents, U. S. Government Printing Office, Washington, D. C., 1964; 3rd printing, with corrections, 1965, pp. 295-329. MR**29**#4914; MR**31**#1400. MR**0177136 (31:1400)****[2]**B. H. Armstrong, "Spectrum line profiles, the Voigt function,"*J. Quant. Spectrosc. Radiat. Transfer*, v. 7, 1967, pp. 61-88.**[3]**B. Lohmander & S. Rittsten, "Table of the function ,"*Kungl. Fysiogr. Sällsk. i. Lund Förh.*, v. 28, 1958, pp. 45-52. MR**20**#1427. MR**0094919 (20:1427)****[4]**D. G. Hummer, "Expansion of Dawson's function in a series of Chebyshev polynomials,"*Math. Comp.*, v. 18, 1964, pp. 317-319. MR**29**#2967. MR**0165687 (29:2967)****[5]**O. Perron,*Die Lehre von den Kettenbrüchen*, Vol. II, 3rd ed., B. G. Teubner, Stuttgart, 1957. MR**19**, 25. MR**0085349 (19:25c)****[6]**H. C. Thacher, Jr., "Computation of the complex error function by continued fractions,"*Blanch Anniversary Volume*, B. Mond (Editor), Aerospace Research Laboratories, Washington, D. C., 1967, pp. 315-337. MR**35**#1423. MR**0211586 (35:2464)****[7]**T. J. Stieltjes,*Oevres Complètes*, Vol. II, Noordhoff, Groningen, 1918, pp. 59-68.**[8]**W. J. Cody & H. C. Thacher, Jr., "Chebyshev approximations for the exponential integral ,"*Math. Comp.*, v. 23, 1969, pp. 289-303. MR**0247736 (40:999)****[9]**W. Gautschi,*Personal Communication*.**[10]**W. J. Cody & J. Stoer, "Rational Chebyshev approximations using interpolation,"*Numer. Math.*, v. 9, 1966, pp. 177-188.**[11]**W. J. Cody, W. Fraser & J. F. Hart, "Rational Chebyshev approximations using linear equations,"*Numer. Math.*, v. 12, 1968, pp. 242-251. MR**1553964**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1970-0258236-8

Keywords:
Rational Chebyshev approximations,
Dawson's integral,
complex error function

Article copyright:
© Copyright 1970
American Mathematical Society