Re: FullSimplify again ...
- To: mathgroup at smc.vnet.net
- Subject: [mg59207] Re: FullSimplify again ...
- From: Detlef Müller <dmueller at mathematik.uni-kassel.de>
- Date: Tue, 2 Aug 2005 00:42:29 -0400 (EDT)
- References: <dcf3d4$lgl$1@smc.vnet.net> <dchnm8$7t2$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Chris wrote:
> Actually, it's not all that strange. If you consider n to be real, the
> expression 0 at anything but a few integers making the function 0
> except for a few holes.
>
> In[43]:=
> FullSimplify[Product[(5-i)/5,{i,1,n}],n\[Element]Integers]
>
> Out[43]:=
> (-1/5)^n*Pochhammer[-4, n]
>
The Problem is that in some works certain polynomials are
written in Hypergeometric Form as infinite Series in wich
factors Pochhammer[-k,n] with natural k,n lead to the
vanishing of all but finitely many coefficients.
The fact that only finitely many coefficients in the
Series are nonzero means, that this hypergeometric function
is a polynomial but of course not that it is zero!
Here The second Argument in Pochhammer[x, n] is seen
as Integer ( Pochhammer[x, n]=x(x+1)...(x+n-1) ).
So the "marginal exceptions" of a few numbers
are of more wight than if we have an exceptional
behaviour for a continous variable at some
point (maybe there are other ways to interpret
it, but in the example we come undoubtly from
a Product).
the behvior is more like if a funktion in a real
variable is wrong on a whole intervall (wich is
nothing, regarding the rest of teh reals ...)
Thats just my feeling here.
Greetings,
Detlef