Problem with Integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg77671] Problem with Integrate*From*: did <didier.oslo at hotmail.com>*Date*: Thu, 14 Jun 2007 06:18:28 -0400 (EDT)

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.