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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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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
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  • 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
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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