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?
>