#86 sum(binomial(2*n-i,i)*binomial(2*n-2*i,n-i),i,0,n)

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nobody
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2010-08-21
2010-08-19
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The following doesn't work in maxima but does work in Mathematica (tested through Wolfram Alpha).

sum(binomial(2*n - i, i)*binomial(2*n - 2*i, n-i), i, 0, n)

The solution is, according to WFA,
Binomial[2 n, n] Hypergeometric2F1[-n, -n, -2 n, -1]

Discussion

  • Dieter Kaiser
    Dieter Kaiser
    2010-08-21

    Maxima can not simplify the example. I think this is not a bug, but a missing feature.
    Moving this bug report to the tracker "Feature requests" and adjusting the title.
    Dieter Kaiser

     
  • Dieter Kaiser
    Dieter Kaiser
    2010-08-21

    • summary: Hypergeometric sum --> sum(binomial(2n-i,i)binomial(2n-2i,n-i),i,0,n)
    • labels: 870406 -->