Re: fundamental Integrate question
- To: mathgroup at smc.vnet.net
- Subject: [mg73053] Re: [mg73031] fundamental Integrate question
- From: Murray Eisenberg <murray at math.umass.edu>
- Date: Wed, 31 Jan 2007 00:24:45 -0500 (EST)
- Organization: Mathematics & Statistics, Univ. of Mass./Amherst
- References: <200701301144.GAA14308@smc.vnet.net>
- Reply-to: murray at math.umass.edu
What's f[z]??? dimitris wrote: > Consider the classical example that incorrectly gave zero in a prior > version of Mathematica > (adopted from http://library.wolfram.com/infocenter/Conferences/5832/) > > In[345]:= > Integrate[f[z], {z, 1 + I, -1 + I, -1 - I, 1 - I, 1 + I}] > Chop[N[%]] > Chop[NIntegrate[f[z], {z, 1 + I, -1 + I, -1 - I, 1 - I, 1 + I}]] > > Out[345]= > 2*I*Pi > > Out[346]= > 6.283185307179586*I > > Out[347]= > 6.2831853071795685*I > > Of course the result is correct considering the pole at origin and the > Residue theorem. > > Trying to understand how Mathematica applies the Newton-Leibniz > formula I just want to know if > I am right below: > > In[511]:= > ((F[z] /. z -> 1 - I) - F[z] /. z -> -1 - I) + ((F[z] /. z -> 1 + I) - > F[z] /. z -> 1 - I) + > ((F[z] /. z -> -1 + I) - F[z] /. z -> 1 + I) + (Limit[F[z], z -> -1, > Direction -> -I] - F[z] /. z -> -1 + I) + > ((F[z] /. z -> -1 - I) - Limit[F[z], z -> -1, Direction -> I]) > > Out[511]= > 2*I*Pi > > Thanks for any response! > > Dimitris > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305
- References:
- fundamental Integrate question
- From: "dimitris" <dimmechan@yahoo.com>
- fundamental Integrate question