Re: fundamental Integrate question
- To: mathgroup at smc.vnet.net
- Subject: [mg73067] Re: fundamental Integrate question
- From: "dimitris" <dimmechan at yahoo.com>
- Date: Thu, 1 Feb 2007 02:58:50 -0500 (EST)
- References: <200701301144.GAA14308@smc.vnet.net><epp6te$djr$1@smc.vnet.net>
f[x_]:=1/x Somehow it failed to appear in the original message! Dimitris Ï/Ç Murray Eisenberg Ýãñáøå: > 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