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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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