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 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul

**References**:**Re: Trouble with Integrate***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>