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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Chebyshev approximations for the exponential integral $ {\rm Ei}(x)$


Authors: W. J. Cody and Henry C. Thacher
Journal: Math. Comp. 23 (1969), 289-303
MSC: Primary 65.25
MathSciNet review: 0242349
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Abstract: The computation of the exponential integral $ Ei(x)$, $ x > 0$, using rational Chebyshev approximations is discussed. The necessary approximations are presented in well-conditioned forms for the intervals $ (0,6]$, $ [6,12]$, $ [12,24]$ and $ [24,\infty )$. Maximal relative errors are as low as from $ 8 \times {10^{ - 19}}to2 \times {10^{ - 21}}$. In addition, the value of the zero of $ Ei(x)$ is presented to 30 decimal places.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1969-0242349-2
PII: S 0025-5718(1969)0242349-2
Article copyright: © Copyright 1969 American Mathematical Society