Dixon's Identity

Author

Eric W. Weisstein
May 19, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/DixonsIdentity.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/DixonsIdentity.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Check

FullSimplify[Table[Sum[(-1)^k*Binomial[n+b,n+k]*Binomial[n+c,c+k]*Binomial[b+c,b+k],{k,-n,n}]==Gamma[b+c+n+1]/(n!*Gamma[b+1]*Gamma[c+1]),{n,-3,3}]]