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Re: Intelligent handling of Infinity in Limits
*To*: mathgroup at smc.vnet.net
*Subject*: [mg7714] Re: Intelligent handling of Infinity in Limits
*From*: Paul Abbott <paul at physics.uwa.edu.au>
*Date*: Wed, 2 Jul 1997 14:21:35 -0400 (EDT)
*Organization*: University of Western Australia
*Sender*: owner-wri-mathgroup at wolfram.com
Locutus Of The Hair Club for Men wrote:
> i was trying to do Integrate[ r^2 Exp[-a r^2], {r,0,Infty}] but MMA
> couldn't simplify a term which clearly was zero.
First, I think instead of Infty you want Infinity:
In[1]:=
2 2
Integrate[r Exp[-a r ], {r, 0, Infinity}]
Out[1]=
Sqrt[Pi] 2 2
If[Re[a] > 0, --------, Integrate[Exp[-a r ] r , {r, 0, Infinity}]]
3/2
4 a
> next i tried integrating over {r,0,r} and then took the limit as r->
>Infty. MMA had the same problem.
In[2]:=
2 2
Integrate[r Exp[-a r ], {r, 0, r}]
Out[2]=
2
Sqrt[Pi] Erf[Sqrt[a] r] Exp[-a r ] r
----------------------- - ------------
3/2 2 a
4 a
You need to load the Limit package:
In[3]:= << Calculus`Limit`
In[4]:= Limit[%%, r -> Infinity]
Out[4]=
Sqrt[Pi]
--------
3/2
4 a
Cheers,
Paul
_________________________________________________________________
Paul Abbott
Department of Physics Phone: +61-8-9380-2734
The University of Western Australia Fax: +61-8-9380-1014
Nedlands WA 6907 paul at physics.uwa.edu.au
AUSTRALIA http://www.pd.uwa.edu.au/Paul
God IS a weakly left-handed dice player
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