Re: Re: Integral: Exp[-(x-m)^2/(2 s^2)] x^3 (1+x^2)^-1
- To: mathgroup at smc.vnet.net
- Subject: [mg52404] Re: [mg52393] Re: [mg52340] Integral: Exp[-(x-m)^2/(2 s^2)] x^3 (1+x^2)^-1
- From: DrBob <drbob at bigfoot.com>
- Date: Fri, 26 Nov 2004 01:04:32 -0500 (EST)
- References: <200411240732.CAA28785@smc.vnet.net> <200411251050.FAA21568@smc.vnet.net>
- Reply-to: drbob at bigfoot.com
- Sender: owner-wri-mathgroup at wolfram.com
I'm thinking I was wrong about divergence; I was looking at computing the integrals using Series and the normal distribution's moment-generating-function, and I got sums that looked divergent -- but that's probably not be the only way to attack it. Bobby On Thu, 25 Nov 2004 05:50:46 -0500 (EST), DrBob <drbob at bigfoot.com> wrote: > All but the first is divergent on -oo to oo, while the first is zero. > > NIntegrate should handle this very well for finite limits. For instance: > > Clear[f] > f[n_Integer][x_] := > (Exp[-(x - m)^2/(2*s^2)]*x^n)/(1 + x^2) > NIntegrate[f[2][x] /. {m -> 0, s -> 1}, {x, -5, 2}] > 0.8149597066587511 > > NIntegrate[f[1][x] /. {m -> 0, s -> 1}, {x, -5, 5}] > > 0. > > Bobby > > On Wed, 24 Nov 2004 02:32:11 -0500 (EST), Opps <*cutinbetweenasterixes*theopps75*evenhere* at *thisalso*yahoo.it> wrote: > >> Hi, >> any suggestion to make the integral of: >> >> Exp[-(x-m)^2/(2 s^2)] x (1+x^2)^-1 >> Exp[-(x-m)^2/(2 s^2)] x^2 (1+x^2)^-1 >> >> Exp[-(x-m)^2/(2 s^2)] x^3 (1+x^2)^-1 >> >> >> >> between -inf and +inf (or indefinite)? >> >> Look like it is not possible, but it is too long time I do not make >> integrals with more advanced techinques (as going to the complex plane)... >> so if you have suggestions (wonderful a solution :) ).... >> >> THANKS >> >> Ale >> >> >> >> >> > > > -- DrBob at bigfoot.com www.eclecticdreams.net
- References:
- Integral: Exp[-(x-m)^2/(2 s^2)] x^3 (1+x^2)^-1
- From: "Opps" <*cutinbetweenasterixes*theopps75*evenhere*@*thisalso*yahoo.it>
- Re: Integral: Exp[-(x-m)^2/(2 s^2)] x^3 (1+x^2)^-1
- From: DrBob <drbob@bigfoot.com>
- Integral: Exp[-(x-m)^2/(2 s^2)] x^3 (1+x^2)^-1