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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
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 $X$.

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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
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Article copyright: © Copyright 1968 American Mathematical Society