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Dixon's Identity

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sum_(k=-n)^n(-1)^k(n+b; n+k)(n+c; c+k)(b+c; b+k)=(Gamma(b+c+n+1))/(n!Gamma(b+1)Gamma(c+1)),

where (n; k) is a binomial coefficient and Gamma(x) is a gamma function.

See also

Dixon's Theorem

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References

Koepf, W. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, pp. 11 and 18-19, 1998.

Referenced on Wolfram|Alpha

Dixon's Identity

Cite this as:

Weisstein, Eric W. "Dixon's Identity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DixonsIdentity.html

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