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Re: Trouble with Integrate

• To: mathgroup at smc.vnet.net
• Subject: [mg39480] Re: Trouble with Integrate
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Wed, 19 Feb 2003 04:41:40 -0500 (EST)
• Organization: The University of Western Australia
• References: <200302070807.DAA26439@smc.vnet.net> <b2agsj$php$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

In article <b2agsj$php$1 at smc.vnet.net>,
 "Marko Vojinovic" <vojinovi at panet.co.yu> wrote:

> Another (rather minor and unrelated) question arises: one can write down the
> result in many various forms using the identity
> 
> Gamma(1+x) = x * Gamma(x)
> 
> (I am not using Mathematica notation here), and FullSimplify knows about
> this identity, but applies it only "from right to left", i.e. 1/2 Gamma(1/2)
> reduces to Gamma(3/2), but never the other way around, which is sometimes
> wanted (in my case, particularly). Since I am not very familiar with
> FullSimplify, is there any way to explain to FullSimplify that I want only
> Gamma[1/4] to appear in the result?

You could use ReplaceRepeated and a replacement rule, e.g. 

   Gamma[5/4] //. Gamma[z_ /; z > 1] :> (z - 1) Gamma[z - 1]

Another rule could be applied to obtain a canonical simplification 
(restricting Gamma[x] to 0 < x < 1).

   Gamma[-11/4] //. Gamma[z_ /; z < 0] :> Gamma[z + 1]/z

It is possible to have such rules applied automatically use $Post.

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
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Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
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• References:
  • Re: Trouble with Integrate
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>