Re: Re: Mathematica Integration help

• To: mathgroup at smc.vnet.net
• Subject: [mg86178] Re: [mg86156] Re: Mathematica Integration help
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Wed, 5 Mar 2008 03:38:24 -0500 (EST)
• References: <fqetdm\$jjs\$1@smc.vnet.net> <fqghfq\$f5c\$1@smc.vnet.net> <200803040707.CAA22493@smc.vnet.net>

```Francogrex wrote:
> On Mar 3, 10:47 am, Jens-Peer Kuska <ku... at informatik.uni-leipzig.de>
> wrote:
>
>>look what happens when you compute from:
>>res = Integrate[
>>   Product[1/(E^((Subscript[x, i] - \[Mu])^2/(2*\[Sigma]^2))*
>>       Sqrt[2*Pi*\[Sigma]^2]), {i, 1, n}], \[Mu]]
>>
>>D[res,\[Mu]]
>>
>>and see that the result is *not*
>>
>>Product[1/(E^((Subscript[x, i] - \[Mu])^2/(2*\[Sigma]^2))*
>>       Sqrt[2*Pi*\[Sigma]^2]), {i, 1, n}]
>>
>>this obvious a bug.
>
>
> The result is:
>
> (1/(E^((\[Mu] - Subscript[x, i])^2/(2*\[Sigma]^2))*Sqrt[\[Sigma]^2]))^
>   n/(2*Pi)^(n/2)
>
> Do you mean that it cannot reconstitute the product?
>

He means that it is a bug. Specifically, the indefinite integral
produced as 'res' is garbage.

This is the same bug that was reported to comp.soft-sys.math.mathematica
by David Cantrell around 6 weeks ago:

http://forums.wolfram.com/mathgroup/archive/2008/Jan/msg00341.html

This has been fixed in the development kernel.

Daniel Lichtblau
Wolfram Research

```