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Mathematics of Computation

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The numerical computation of two transcendental functions related to the exponential integral


Author: D. M. Chipman
Journal: Math. Comp. 26 (1972), 241-249
MSC: Primary 65D20
DOI: https://doi.org/10.1090/S0025-5718-1972-0298885-6
MathSciNet review: 0298885
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Abstract: Algorithms for the computation of numerical values of the two transcendental functions

$\displaystyle \int_0^x {\tfrac{1}{t}} [\operatorname{Ei} (t) - \gamma - \ln \le... ...} [\operatorname{Ei} (t) - \gamma - \ln \left\vert t \right\vert]\exp ( - t)dt,$

where $ \gamma $ is Euler's constant and $ \operatorname{Ei} (t)$ is the exponential integral, are presented for all ranges of the real variable $ x$. A table of values of these functions is also given.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1972-0298885-6
Keywords: Integrals of exponential integral, integrals of logarithm integral, exponential integral, logarithm integral
Article copyright: © Copyright 1972 American Mathematical Society