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MathGroup Archive 2005

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Re: Solving an integral in the limit.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62417] Re: Solving an integral in the limit.
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 23 Nov 2005 06:27:28 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <dm11o7$e0s$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

when the integrand is extended into the complex plane,
one may be able to compute the defined integral without
finding the undefined integral and take the limit.

Regards
  Jens

"Josef Karthauser" <joe at tao.org.uk> schrieb im 
Newsbeitrag news:dm11o7$e0s$1 at smc.vnet.net...
| I'm having trouble solving a complicated 
integral using mathematica,
| and I'm looking for some wisdom on the matter.
|
| The problem can be summarised as follows. 
Mathematica can determine
| the solution to,
|
|    Integrate[E^(I*x^2)/ Sqrt[1 + x^2], {x, 0, 
Infinity}]
|
| but if I replace the upper bound with a free 
variable and take the limit
| as it goes to Infinity mathematica doesn't 
manage it,
|
|    Limit[Integrate[E^(I*x^2)/ Sqrt[1 + x^2], {x, 
0, a}], a -> Infinity]
|
| Surely it should be able to determine that the 
answer is the same as in
| the previous case.  Is there anyway to pursuade 
it?
|
| Many thanks,
| Joe
| -- 
| Josef Karthauser (joe at tao.org.uk) 
http://www.josef-k.net/
| FreeBSD (cvs meister, admin and hacker) 
http://www.uk.FreeBSD.org/
| Physics Particle Theory (student) 
http://www.pact.cpes.sussex.ac.uk/
| ================ An eclectic mix of fact and 
theory. =================
| 



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