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Re: Inconsistent behavior?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg87285] Re: [mg87243] Inconsistent behavior?
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sun, 6 Apr 2008 06:45:16 -0400 (EDT)
  • References: <200804050923.EAA12082@smc.vnet.net>

Binomial[n,r] is automatically expanded only for small values of r.  
For large ones you need to use FunctionExpand:

FunctionExpand[Binomial[n, 11]]
((n - 10)*(n - 9)*(n - 8)*(n - 7)*(n - 6)*(n - 5)*
      (n - 4)*(n - 3)*(n - 2)*(n - 1)*n)/39916800

(The distinction between "small" and "large" numbers is a little  
problematic logically, since one can "prove" by induction that all  
positive integers are small, assuming that 1 is small and  "n is small  
-> (n+1) is small", but as a matter of practice it seems a sensible  
idea.)

Andrzej Kozlowski


On 5 Apr 2008, at 10:23, angela wrote:
> Binomial[n,4] yields
> 1/24 (-3+n) (-2+n) (-1+n) n
>
> Binomial[n,5] yields
> 1/120 (-4+n) (-3+n) (-2+n) (-1+n) n
>
> Binomial[n,6] yields
> Binomial[n,6]
>
> Binomial[n,7] yields
> Binomial[n,7]
>
> Is some setting doing this.
>
> Thanks;
> Angela
>



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