[Octave-bug-tracker] [bug #47738] expint is inaccurate for certain imaginary inputs

[Marco Caliari]

Follow-up Comment #7, bug #47738 (project octave):

Dear all,

some time ago I made some experiments with expint. I implemented four formulas
that I found on Abramowitz&Stegun and Numerical Recipes in Fortran77. The
result was that the classical series expansion (Abramowitz 5.1.11) was the
most accurate in the region around the segment [-40,0] in the complex plane.
The continued fraction expansion (Abramowitz 5.1.22) or its modification
(Numerical Recipes) was the most accurate elsewhere. In the computational
algorithm proposed by Numerical Recipes, they use the continued fraction
expansion and, if it fails, they use the series.

I do not remember the details now, but I attach my experiments.
exponential_integral.m computes the values in the four ways, expint.ref
contains reference values (Octave's binary format) and testexpint.m compare
the results.

(file #37040, file #37041, file #37042)
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Additional Item Attachment:

File name: expint.ref                     Size:64 KB
File name: exponential_integral.m         Size:2 KB
File name: testexpint.m                   Size:0 KB


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