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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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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


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 $X$.
  • 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
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Additional Information
  • © Copyright 1968 American Mathematical Society
  • Journal: Math. Comp. 22 (1968), 641-649
  • MSC: Primary 65.25
  • DOI:
  • MathSciNet review: 0226823