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Re: variable declarations in mathematica?

• To: mathgroup at smc.vnet.net
• Subject: [mg7415] Re: [mg7373] variable declarations in mathematica?
• From: jpk at max.mpae.gwdg.de
• Date: Sat, 31 May 1997 15:07:24 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

> I'm trying to get Mathematica 3.0 to treat the variable n as an integer during 
the
> simplification process. I spent several hours with the mathematica handbook, 
but have not yet
> found the solution.
> 
> What I want is to somehow DEFINE n as an integer so that for instance:
> 
>  Gamma[ n ]            simplifies to:        ( n - 1 )!            or,
> 
>                                              ( 2 n - 1 )!!
>  Gamma[ n + 1/2 ]      simplifies to:        ------------- . Sqrt[ Pi ]
>                                                   2^n
> 
> It cannot be hard...
> 
> Thanks.
> 
> Bas ten Hoope
> 
> 
Hi here is one solution

First say n is an integer 

n/: IntegerQ[n]:=True

Than say that Gamma[_?IntegerQ] is (n-1)! and add some rules for sums and
products of integers

Unprotect[Gamma,IntegerQ]
IntegerQ[a_+b_]:=IntegerQ[a] && IntegerQ[b]
IntegerQ[a_*b_]:=IntegerQ[a] && IntegerQ[b]	
Gamma[n_?IntegerQ]:=(n-1)!
Protect[Gamma,IntegerQ]

and 
Gamma[n] is simplifyed as You want.

Hope that helps
Jens