Evaluation of complex functions

From: Herman Rubin (hrubin_at_odds.stat.purdue.edu)
Date: 12/16/04 

Date: 16 Dec 2004 15:07:04 -0500

I am interested in reasonably quick and accurate algorithms
to evaluate, quickly and accurately, certain complex functions
of a complex variable. These functions are real on the
positive real axis (sometimes negative real axis as well),
and it is wanted to get both the real and imaginary part
accurate to floating precision, including for the imaginary
part of the argument small, for the function, and the
imaginary part for the derivative.

The family will increase, but at this time, the functions
I am considering are ln(Gamma(z)), and here it is needed
that for Re(z) < 0, the continuous branch of the logarithm
is taken, and the other one is \int_0^z ((exp(t) - 1)/t dt.
If I find the application useful, the algorithms need to
be reasonably fast, not using numerical integration. 

-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558
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