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Q: Contour integral

• To: mathgroup@smc.vnet.net
• Subject: [mg10792] Q: Contour integral
• From: Patrick Van Esch <pvanesch@vub.ac.be>
• Date: Thu, 5 Feb 1998 00:58:36 -0500
• Organization: Vrije Universiteit Brussel

Hi folks,

I have the following question:  I've been reading "Mathematica for
scientists and engineers", and there is an example on how to calculate
numerically a contour integral:

 NContourIntegrate[f_,par:(z_->g_),{t_,a_,b_}]:=
 NIntegrate[Evaluate[(f/.par)D[g,t]],{t,a,b}]

When applying this to a limacon:

NContourIntegrate[1/(z-1/2),z->Exp[I t](2Cos[t]+1),{t,0,2 Pi}]

one gets the right answer:

\!\(3.33066907387546962`*^-16 + 12.5663706143520892`\ I\)

(4pi I)

However, when modifying the numerical integration into an analytic one,
ContourIntegrate[f_,par:(z_->g_),{t_,a_,b_}]:=
 Integrate[Evaluate[(f/.par)D[g,t]],{t,a,b}]

The answer that is obtained is wrong:

2 Pi I

Any ideas ?

cheers,
Patrick.

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