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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
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.

References [Enhancements On Off] (What's this?)

  • [1] A. Erdélyi, W. Magnus, F. Oberhettinger & F. Tricomi, Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York, 1953, pp. 143-144. MR 15, 419.
  • [2] D. M. Chipman & J. O. Hirschfelder, J. Chemical Physics (To appear.)
  • [3] M. Geller & E. W. Ng, ``A table of integrals of the exponential integral,'' J. Res. Nat. Bur. Standards Sect. B, v. 73B, 1969, pp. 191-210. MR 40 #2910. MR 0249669 (40:2910)
  • [4] 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.
  • [5] P. Wynn, ``The rational approximation of functions which are formally defined by a power series expansion,'' Math. Comp., v. 14, 1960, pp. 147-186. MR 22 #7244. MR 0116457 (22:7244)

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Keywords: Integrals of exponential integral, integrals of logarithm integral, exponential integral, logarithm integral
Article copyright: © Copyright 1972 American Mathematical Society

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