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

```

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