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 _________________________________________________________________