Abel's Binomial Theorem

Author

Eric W. Weisstein
January 16, 2009

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Calculus/AbelsBinomialTheorem.nb.

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

©2009 Wolfram Research, Inc. except for portions noted otherwise

Identity

Sum[Binomial[m,y](((w+m-y))^(m-y-1))(((z+y))^y),{y,0,m}]

Subtract@@@Table[{Sum[Binomial[m,y](((w+m-y))^(m-y-1))(((z+y))^y),{y,0,m}],((((z+w+m))^m)/w)},{m,10}]//Expand//Union