RE: Exponential Integral (UNCLASSIFIED)

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

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