Re: Re: problem with double integral - Very useful for

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• Subject: [mg107676] Re: [mg107669] Re: problem with double integral - Very useful for
• From: smcconne at pi0.physi.uni-heidelberg.de
• Date: Mon, 22 Feb 2010 19:03:48 -0500 (EST)
• References: <hlj3vf\$rop\$1@smc.vnet.net>

I just thought it might be useful to highlight this post for searching purposes because this kind of NIntegrate workaround is extremely handy when dealing with a 3 body problem. Specifically because in the three body problem one frequently uses a multipole expansion for the distance between 2 of the particles and the centre of the frame of reference (usually the 3rd particle).

The expansion is Sum[((Min[r,R]^l)/(Max[r,R])^(l+1))LegendreP[Cos[[/gamma]]],{l,0,Infinity}]. Of course this two variable expansion usually becomes a part of an integral which is split in order to "simplify" things, but if you don't tell NIntegrate that the arguments are numeric, it will hardly seem like a simplification at all.

I hope many researchers on 3 body systems who conduct a search for how to wedge Mathematica into performing this integral find this thread!!

Sean.

Quoting dh <dh at metrohm.com>:

> Hi Regina,
> you may do it like:
>
> fun[Q_?NumericQ]:= NIntegrate[(Exp[-1/(4 x) - 4 x]), {x, Q, \[Infinity]}]
> NIntegrate[1/fun[x], {x, 0, 1}]
>
> Note that I changed the order of the limits and defined fun only for
> numerical arguments. Otherwise NIntegrate is not happy.
> Daniel
>
>
>
> On 18.02.2010 11:15, Regina wrote:
>> Hi there,
>> i got a problem: how can i evaluate the following integral:
>> define:
>> i[Q_] := Integrate[(Exp[-a/(4 x) - 4 x]), {x, \[Infinity], Q}]
>> now i want to compute:
>> NIntegrate[1/i[Q], {Q, 0, 1}]
>>
>> what am i doing wrong? how can i integrate that function?
>>
>
>
> --
>
> Daniel Huber
> Metrohm Ltd.
> Oberdorfstr. 68
> CH-9100 Herisau
> Tel. +41 71 353 8585, Fax +41 71 353 8907
> E-Mail:<mailto:dh at metrohm.com>
> Internet:<http://www.metrohm.com>
>
>

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