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MathGroup Archive 2001

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Re: Possible Incorrect Summation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31054] Re: [mg31034] Possible Incorrect Summation
  • From: Andrzej Kozlowski <andrzej at bekkoame.ne.jp>
  • Date: Sat, 6 Oct 2001 03:32:22 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I am not sure how you can see it by graphing the difference, since:

In[52]:=
FullSimplify[
   Sum[ (-1)^k Binomial[2 n, k] Binomial[2k, k] Binomial[4n - 2k, 2n -
k],{k,0,2n}]-Binomial[2n,n]^2,Element[n,Integers]]

Out[52]=
0

Also:

In[54]:=
Union[Table[
     Sum[ (-1)^k Binomial[2 n, k] Binomial[2k, k] Binomial[4n - 2k, 2n -
k],{k,0,2n}]-Binomial[2n,n]^2,{n,1,100}]]

Out[54]=
{0}



On Friday, October 5, 2001, at 02:22  PM, Richard Palmer wrote:

>
> I believe
>
>     Sum[ (-1)^k Binomial[2 n, k] Binomial[2k, k] Binomial[4n - 2k, 2n -
> k],{k,0,2n}]
>
>  is a special case of Dixon's Identity and should equal 
> Binomial[2n,n]^2.
> Previously the SymbolicSum package returned a value which could be
> simplified to the result.  The latest version of Mathematica returns a 
> value
> which is is not this result as can be seen by graphing the difference.  
> What
> has changed?
>
>
>
>
>
Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/



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