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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
>
>
>
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