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## RE: [Axiom-mail] Exponential Integral (UNCLASSIFIED)

**From**: |
Segletes, Steven (Civ,ARL/WMRD) |

**Subject**: |
RE: [Axiom-mail] Exponential Integral (UNCLASSIFIED) |

**Date**: |
Tue, 18 Aug 2009 09:49:51 -0400 |

Classification: UNCLASSIFIED
Caveats: NONE
Tim,
I have attached a PDF writeup detailing the more accurate fits to E1(x),
relative to those presented in ARL-TR-1758. My actual fits are to F1 =
[x exp(x) E1(x)] which spans a functional range from 0 to 1. The best
accuracy I have been yet able to achieve, defined by limiting the value
of [(F1)_fit - F1]/F1 over the domain, is approximately 3.1E-07 with a
12-parameter fit, which unfortunately isn't quite to 32-bit
floating-point accuracy. Nonetheless, the fit is not a piecewise fit,
but rather a single continuous function over the domain of nonnegative
x, which avoids some of the problems associated with piecewise domain
splicing.
Also, I have not, as yet, had the need to look at other functions that
could stand improved fitting, but you could always suggest a function to
get me thinking about it.
Kindest regards,
Steven Segletes
US Army Research Laboratory
Aberdeen Proving Ground, MD 21005-5066
Classification: UNCLASSIFIED
Caveats: NONE

**
**`E1.pdf`

*Description:* E1.pdf