Re: Simplify using assumptions and Gamma[*]

*To*: mathgroup at smc.vnet.net*Subject*: [mg34752] Re: [mg34743] Simplify using assumptions and Gamma[*]*From*: Andrzej Kozlowski <andrzej at tuins.ac.jp>*Date*: Wed, 5 Jun 2002 03:38:09 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Mathematica considers the factorial function z! to be defined for all complex values z and equal to Gamma[z+1] without any restrictions on z: In[34]:= FullSimplify[Gamma[z+1]==z! ] Out[34]= True No assumptions are needed. This is just a matter fo definition of course. FullSimplify will not replace Gamma[z] by (z-1)! but it will do the opposite: In[35]:= FullSimplify[(z-1)!] Out[35]= Gamma[z] Obviously this is again a matter of choice. If you would like FullSimplify to transform Gamma[z+1] to z! you can add a transformation function to FullSimplify: f[Gamma[z_ + 1]] := z! In[37]:= FullSimplify[Gamma[z+1],TransformationFunctions->{Automatic,f}] Out[37]= z! Andrzej Kozlowski Toyama International University JAPAN http://platon.c.u-tokyo.ac.jp/andrzej/ On Tuesday, June 4, 2002, at 04:41 PM, Michael Chang wrote: > Hi, > > Since the Euler Gamma function is (n-1)! for n>=1 and n an integer, I > was wondering why > > FullSimplify[Gamma[n], n>=1 && n \[Element] Integers] > > does not evaluate to (n-1)! ? Am I missing something here? > > Am I using the Assumptions capability incorrectly? > > Many thanks in advance, > > Michael > > >