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Problem with Integrate


Consider the Cauchy integral around the unit circle
of f(z)=z, and compute the integral for the angle t
varying from T to T+2*Pi, and for a z inside the
circle. For example:

In[1]:=  T = -Pi;
           z = 1/4*Exp[I*Pi];
           FullSimplify[ Integrate[ Exp[2*I*t]/(Exp[I*t]-z),{t,0+T,2*Pi
+T}] - 2*Pi*z]

Out[3]=  0

which is the expected result. Correct results were obtained for all
the numerical
values of T I tried. But if I give T a literal value, say T=a,
I get a wrong answer, e.g.

In[4]:=  T = a;
           z = 1/4*Exp[I*Pi];
           FullSimplify[ Integrate[ Exp[2*I*t]/(Exp[I*t]-z),{t,0+T,2*Pi
+T}] - 2*Pi*z]

Out[6]= \!\(=CF=80\/2\)

This was obtained on Mathematica 5.2 and 6.0, run by Windows XP.



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