From bug-octave-request at bevo dot che dot wisc dot edu  Tue Sep  5 09:58:34 2000
Subject: lgamma bug on real negative axis
From: Rolf Fabian <fabian at tu-cottbus dot de>
To: "'bug-octave UWISC'" <bug-octave at bevo dot che dot wisc dot edu>
Date: Tue, 5 Sep 2000 09:59:11 -0500 (CDT)

Hi,

one conclusiion from the uploads to the help-list
<http://www.che.wisc.edu/octave/mailing-lists/help-octave/2000/1114>
<http://www.che.wisc.edu/octave/mailing-lists/help-octave/2000/1115>

is that lgamma returns incorrect output on the negative real axis
for the intervals (0..-1) , (-2..-3) ,( -4..-5) etc.. ,  in general  ( -(EVEN N).. -(N+1) )
because the necessary imaginary part ( +pi*i ) seems to be discarded from output!

This bug was observed for V2.0.13 cygwin  - win95 (precompiled)
V2.1.14 OS/2 and V2.1.31 ( Thanks to Paul Kienzle and Dirk Laurie for testing!).

Repeat by e.g. 
:)  log(gamma(x=-1/2:-1:-5)).'
ans =
   1.26551 + 3.14159i
   0.86005 + 0.00000i
  -0.05624 + 3.14159i
  -1.30901 + 0.00000i
  -2.81308 + 3.14159i

:) lgamma(x).'
ans =
   1.265512
   0.860047
  -0.056244
  -1.309007
  -2.813084

There's also a typo (sorry) in my previous upload
http://www.che.wisc.edu/octave/mailing-lists/help-octave/2000/1114
concerning the sign of the imaginary parts, which needs to be corrected.
Correctly you should read

Both -pi*i and +pi*i are actually possible, because
the complex EXPONENTIAL function is periodical with a
period of 2*pi*i, so that the sign depends on some
(more or less arbitrary) definition. 

Rolf



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