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: owner-wri-mathgroup at wolfram.com
This looks like a bug, although Mathematica's Integrate is in general
unreliable when dealing with non-analytic 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.u-tokyo.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
>
>