Rational Chebyshev approximations for the exponential integral

Authors:
W. J. Cody and Henry C. Thacher

Journal:
Math. Comp. **22** (1968), 641-649

MSC:
Primary 65.25

DOI:
https://doi.org/10.1090/S0025-5718-1968-0226823-X

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 continued-fraction expansion for small .

**[1]***Handbook of mathematical functions, with formulas, graphs, and mathematical tables*, Edited by Milton Abramowitz and Irene A. Stegun. Third printing, with corrections. National Bureau of Standards Applied Mathematics Series, vol. 55, Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1965. MR**0177136****[2]**E. E. Allen, ``Note 169,''*MTAC*, v. 8, 1954, p. 240.**[3]**Cecil Hastings Jr.,*Approximations for digital computers*, Princeton University Press, Princeton, N. J., 1955. Assisted by Jeanne T. Hayward and James P. Wong, Jr. MR**0068915****[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. 401-403.**[7]**W. J. Cody & J. Stoer, ``Rational Chebyshev approximations using interpolation,''*Numer. Math.*, v. 9, 1966, pp. 177-188.**[8]**Peter Henrici,*Some applications of the quotient-difference algorithm*, Proc. Sympos. Appl. Math., Vol. XV, Amer. Math. Soc., Providence, R.I., 1963, pp. 159–183. MR**0159415**

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DOI:
https://doi.org/10.1090/S0025-5718-1968-0226823-X

Article copyright:
© Copyright 1968
American Mathematical Society