Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2002
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2002

[Date Index] [Thread Index] [Author Index]

Search the Archive

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
>
>
>



  • Prev by Date: RE: How can solue the inequation system in mathematica
  • Next by Date: Re: Cut and paste: General rules ?
  • Previous by thread: Re: Simplify using assumptions and Gamma[*]
  • Next by thread: Re: Simplify using assumptions and Gamma[*]