Rational Chebyshev approximations for the exponential integral $E_{1} (x)$

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 ${E_1}(x)$ 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.),
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E. E. Allen, “Note 169,” - 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**
C. Hastings, Jr., “Note 143,” - 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**

*MTAC*, v. 8, 1954, p. 240.

*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.

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Article copyright:
© Copyright 1968
American Mathematical Society