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Mathematics of Computation

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



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
MathSciNet review: 0298885
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Abstract: Algorithms for the computation of numerical values of the two transcendental functions \[ \int _0^x {\tfrac {1}{t}} [\operatorname {Ei} (t) - \gamma - \ln \left | t \right |]dt\quad {\text {and}}\quad \int _0^x {\tfrac {1}{t}} [\operatorname {Ei} (t) - \gamma - \ln \left | t \right |]\exp ( - t)dt,\] 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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Keywords: Integrals of exponential integral, integrals of logarithm integral, exponential integral, logarithm integral
Article copyright: © Copyright 1972 American Mathematical Society