Re: Unexpected condition on convergence of integral
- To: mathgroup at smc.vnet.net
- Subject: [mg67306] Re: [mg67293] Unexpected condition on convergence of integral
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Sat, 17 Jun 2006 04:36:30 -0400 (EDT)
- Reply-to: hanlonr at cox.net
- Sender: owner-wri-mathgroup at wolfram.com
Appears to work if you divide the interval
expr=1/(1+(x-y)^2);
Integrate[expr,{y,-Infinity,x}]+
Integrate[expr,{y,x,Infinity}]
Pi
Bob Hanlon
---- Andrew Moylan <andrew.moylan at anu.edu.au> wrote:
> Integrate[1 / (1 + (x - y)^2), {y, -Infinity, Infinity}] yields If[Im[x] != 0, Pi, ...], but (I think) this integral should converge to Pi unconditionally (try it for some real values of x).
>
> Using the option "Assumptions -> Im[x] == 0" in Integrate[] further yields the following warning: "Integral of [bla] does not converge on {-Infinity, Infinity}".
>
> Can anyone shed some light on why Integrate can't determine that this integral converges for all x?
>