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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