Rational Chebyshev approximations for the exponential integral $E_{1} (x)$
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- by W. J. Cody and Henry C. Thacher PDF
- Math. Comp. 22 (1968), 641-649 Request permission
Abstract:
Rational Chebyshev approximations are presented for the exponential integral ${E_1}(x)$ in the intervals $(0,1]$, $[1,4]$, and $[4,\infty )$ with maximal relative errors ranging down to ${10^{ - 21}}$. $25S$ coefficients are also given for a continued-fraction expansion for small $X$.References
- Milton Abramowitz (ed.), Handbook of mathematical functions, with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, No. 55, U. S. Government Printing Office, Washington, D.C., 1965. Superintendent of Documents. MR 0177136 E. E. Allen, “Note 169,” MTAC, v. 8, 1954, p. 240.
- 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, DOI 10.1515/9781400875597 C. Hastings, Jr., “Note 143,” MTAC, v. 7, 1953, p. 68. 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. W. Fraser & J. F. Hart, “On the computation of rational approximations to continuous functions,” Comm. ACM, v. 5, 1962, pp. 401–403. W. J. Cody & J. Stoer, “Rational Chebyshev approximations using interpolation,” Numer. Math., v. 9, 1966, pp. 177–188.
- 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
Additional Information
- © Copyright 1968 American Mathematical Society
- 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