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MathGroup Archive 2003

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Re: Improper integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44624] Re: Improper integral
  • From: vb at cybertester.com (Vladimir Bondarenko)
  • Date: Tue, 18 Nov 2003 06:41:54 -0500 (EST)
  • References: <bpa2sm$1eh$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

poujadej at yahoo.fr (Jean-Claude Poujade) wrote in message news:<bpa2sm$1eh$1 at smc.vnet.net>...
> Bonjour le groupe,
> 
> I'm not a mathematician and I wonder why Mathematica doesn't return 0 
> for this doubly infinite improper integral :
> 
> In[1]:=$Version
> Out[1]=4.1 for Microsoft Windows (November 2, 2000)
> 
> In[2]:=Integrate[x/(1+x^2),{x,-Infinity,Infinity},PrincipalValue->True]
> Integrate::idiv[...]does not converge[...]
> Out[2]:=Integrate[x/(1+x^2),{x,-Infinity,Infinity},PrincipalValue->True]
> 
> maybe it's different with Mathematica 5.0 ?
> ---
> jcp


Bonjour,

JCP> why Mathematica doesn't return 0

This is a bug.

JCP> maybe it's different with Mathematica 5.0 ?

No news, good news ;)

In[1] := $Version

Out[1] = 5.0 for Microsoft Windows (June 11, 2003)

In[2] := Integrate[x/(1 + x^2), {x, -Infinity, Infinity}, \
         PrincipalValue -> True]

         Integrate::"idiv" : Integral of x/(1 + x^2) does not
         converge on {-Infinity, Infinity}

         Integrate[x/(1 + x^2), {x, -Infinity, Infinity}, 
         PrincipalValue -> True]

My prediction for you is that, by a subtle reason, this 
behaviour will be fixed in Mathematica 6 or earlier.


Cheers,

Vladimir Bondarenko

http://www.cybertester.com/


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