Rational Chebyshev approximations for the exponential integral
Authors:
W. J. Cody and Henry C. Thacher
Journal:
Math. Comp. 22 (1968), 641649
MSC:
Primary 65.25
MathSciNet review:
0226823
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Abstract: Rational Chebyshev approximations are presented for the exponential integral in the intervals , , and with maximal relative errors ranging down to . coefficients are also given for a continuedfraction expansion for small .
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C. Hastings, Jr., ``Note 143,'' MTAC, v. 7, 1953, p. 68.
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W. Fraser & J. F. Hart, ``On the computation of rational approximations to continuous functions,'' Comm. ACM, v. 5, 1962, pp. 401403.
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W. J. Cody & J. Stoer, ``Rational Chebyshev approximations using interpolation,'' Numer. Math., v. 9, 1966, pp. 177188.
 [8]
Peter
Henrici, Some applications of the quotientdifference
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(28 #2632)
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 W. Gautschi & W. F. Cahill, ``Exponential integral and related functions,'' Chapter 5 in Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, edited by M. Abramowitz &I. A. Stegun, Nat. Bur. Standards Appl. Math. Series, 55, Superintendent of Documents, U. S. Government Printing Office, Washington, D. C., 1964; 3rd printing, with corrections, 1965. MR 29 #4914; MR 31 #1400. MR 0177136 (31:1400)
 [2]
 E. E. Allen, ``Note 169,'' MTAC, v. 8, 1954, p. 240.
 [3]
 C. Hastings, Jr., Approximations for Digital Computers, Princeton Univ. Press, Princeton, N. J., 1955, pp. 188190. MR 16, 963. MR 0068915 (16:963e)
 [4]
 C. Hastings, Jr., ``Note 143,'' MTAC, v. 7, 1953, p. 68.
 [5]
 C. W. Clenshaw, Chebyshev Series for Mathematical Functions, National Physical Laboratorv Math. Tables, Vol. 5, Department of Scientific and Industrial Research, H.M.S.O., London, 1962. MR 26 #362.
 [6]
 W. Fraser & J. F. Hart, ``On the computation of rational approximations to continuous functions,'' Comm. ACM, v. 5, 1962, pp. 401403.
 [7]
 W. J. Cody & J. Stoer, ``Rational Chebyshev approximations using interpolation,'' Numer. Math., v. 9, 1966, pp. 177188.
 [8]
 P. Henrici, ``Some applications of the quotient difference algorithm'' in High Speed Computing and Experimental Arithmetic, Proc. Sympos. Appl. Math., Vol. 15, Amer. Math. Soc., Providence, R. I., 1963, pp. 159183. MR 28 #2632. MR 0159415 (28:2632)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571819680226823X
PII:
S 00255718(1968)0226823X
Article copyright:
© Copyright 1968
American Mathematical Society
