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MathGroup Archive 2001

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Possible Incorrect Summation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31034] Possible Incorrect Summation
  • From: Richard Palmer <mapsinc at bellatlantic.net>
  • Date: Fri, 5 Oct 2001 01:22:45 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

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?




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