The numerical computation of two transcendental functions related to the exponential integral
Author:
D. M. Chipman
Journal:
Math. Comp. 26 (1972), 241249
MSC:
Primary 65D20
DOI:
https://doi.org/10.1090/S00255718197202988856
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.

A. Erdélyi, W. Magnus, F. Oberhettinger & F. Tricomi, Higher Transcendental Functions, Vol. 2, McGrawHill, New York, 1953, pp. 143144. MR 15, 419.
D. M. Chipman & J. O. Hirschfelder, J. Chemical Physics (To appear.)
 Murray Geller and Edward W. Ng, A table of integrals of the exponential integral, J. Res. Nat. Bur. Standards Sect. B 73B (1969), 191–210. MR 249669 I. S. Gradšeĭn & I. M. Ryžik, Tables of Integrals, Series and Products, Fizmatgiz, Moscow, 1963; English transl., Academic Press, New York, 1965, pp. 574, 334, 532. MR 28 #5198; MR 33 #5952.
 P. Wynn, The rational approximation of functions which are formally defined by a power series expansion, Math. Comput. 14 (1960), 147–186. MR 0116457, DOI https://doi.org/10.1090/S00255718196001164572
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Keywords:
Integrals of exponential integral,
integrals of logarithm integral,
exponential integral,
logarithm integral
Article copyright:
© Copyright 1972
American Mathematical Society