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Re: Inconsistent behavior?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg87281] Re: Inconsistent behavior?
  • From: "David Park" <djmpark at comcast.net>
  • Date: Sun, 6 Apr 2008 06:44:31 -0400 (EDT)
  • References: <ft7ggo$bs3$1@smc.vnet.net>

Angela,

Binomial is one of the functions that Mathematica knows quite a bit about. 
The Function help page talks about evaluation to exact results with integers 
and 'certain other special arguments'. Maybe Mathematica doesn't expand 
Binomial[n, m_Integer] when m >5 because users might prefer to keep the 
shorter unevaluated form in symbolic expressions. In any case, you can 
expand by using FunctionExpand.

Binomial[n, 20] // FunctionExpand
((-19 + n) (-18 + n) (-17 + n) (-16 + n) (-15 + n) (-14 + n) (-13 +
     n) (-12 + n) (-11 + n) (-10 + n) (-9 + n) (-8 + n) (-7 + n) (-6 +
      n) (-5 + n) (-4 + n) (-3 + n) (-2 + n) (-1 +
     n) n)/2432902008176640000

But it is a little inconsistent to have an arbitrary break off point and not 
mention it. It might be more consistent to evaluate none of these cases or 
only m = 0 and m = 1.

-- 
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/


"angela" <mpopyft at lycos.com> wrote in message 
news:ft7ggo$bs3$1 at smc.vnet.net...
> 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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