#2318 Contour integral apparently depends on center of circle

[Anonymous]

See the following sage-support thread: http://groups.google.com/group/sage-support/browse_thread/thread/3aee0a551bfac1d9/a0143d963486e38f

Apparently this integral evaluation depends on what circle containing the (only) pole one uses. I haven't checked the math by hand personally, just reporting.

Maxima 5.25.1 http://maxima.sourceforge.net
using Lisp SBCL 1.0.24
Distributed under the GNU Public License. See the file COPYING.
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The function bug_report() provides bug reporting information.
(%i1) f(z):=(z-%i)*(z-1)^2/(z-(-1/2-%i/3));
2
(z - %i) (z - 1)
(%o1) f(z) := -----------------
- 1 %i
z - (--- - --)
2 3
(%i2) display2d:false;

(%o2) false
(%i3) integrate(f(-1/2-%i/3+exp(%i*t))*%i*exp(%i*t),t,0,2*%pi);

(%o3) %i*((4*%i-13)/3-((724*%i-57)*%pi+144*%i-468)/108)
(%i4) expand(ratsimp(%i*((4*%i-13)/3-((724*%i-57)*%pi+144*%i-468)/108)));

(%o4) 19*%i*%pi/36+181*%pi/27
(%i5) integrate(f(2*exp(%i*t))*2*%i*exp(%i*t),t,0,2*%pi);

(%o5) 0