The efficient computation of some generalised exponential integrals

  • Authors:

  • Allan J. MacLeod

  • Affiliations:

  • Department of Mathematics and Statistics, University of Paisley, High Street, Paisley PA1 2BE, Scotland, UK

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2002

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Abstract

The accurate and efficient computation of the special functions Gk(x) is discussed, where Gk(x) = 1/(k-1)! ∫∞1 exp(-xy)(log y)k-1 dy/y. These functions appear in the computation of the derivatives of the L-series of an elliptic curve, and in radiative transfer problems from astrophysics. By dividing (0, ∞) into 3 sub-intervals, we derive Chebyshev polynomial expansions for Gk, k = 1,...,4 with the coefficients given to an accuracy of 20 decimal places.