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Re: Different Integration Results
 To: mathgroup at smc.vnet.net
 Subject: [mg30358] Re: [mg30344] Different Integration Results
 From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
 Date: Sun, 12 Aug 2001 02:29:48 0400 (EDT)
 Sender: ownerwrimathgroup at wolfram.com
This looks like a bug, although Mathematica's Integrate is in general
unreliable when dealing with nonanalytic functions (in the complex
plane). Fortunately there are usually several different approaches which
one should use to confirm the answer. In your case the following two
both give 1:
In[24]:=
z=Integrate[rho[x],x]
Out[24]=
19 19 5 5 49
ArcTan[x] 7
18 (()   +  +    + 
ArcTan[2 x])
12 (I + x) 12 (I + x) 6 (I + 2 x) 6 (I + 2 x)
18 9
()
35 Pi
In[25]:=
Limit[z, x > Infinity]
Out[25]=
1

2
In[11]:=
Limit[z, x > Infinity]
Out[11]=
1
()
2
Alternatively, the following also gives the right answer:
In[35]:=
Integrate[TrigToExp[rho[x]],{x,Infinity,Infinity}]
Out[35]=
1
Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.utokyo.ac.jp/andrzej/
On Saturday, August 11, 2001, at 04:40 PM, Harald Grossauer wrote:
>
> Hi,
> I have got a problem with the attached notebook. In the last two lines,
> if I use Integrate[ ] the result is 99/35, NIntegrate[ ] says it is
> "1.". Due to the nature of the problem (quantum theory, fourier
> transform) I would expect the result to be 1 exactly. What could cause
> this difference?
> Greetings, Harald
>
>
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