Abel's binomial theorem, named after Niels Henrik Abel, is a mathematical identity involving sums of binomial coefficients. It states the following:
| m | |
| \sum | |
| k=0 |
\binom{m}{k}(w+m-k)m-k-1(z+k)k=w-1(z+w+m)m.
\begin{align} &{} \binom{2}{0}(w+2)1(z+0)0+\binom{2}{1}(w+1)0(z+1)1+\binom{2}{2}(w+0)-1(z+2)2\\ &=(w+2)+2(z+1)+
| (z+2)2 | |
| w |
\\ &=
| (z+w+2)2 | |
| w |
. \end{align}