Abel's binomial theorem

Abel's binomial theorem, named after Niels Henrik Abel, states the following:

$\sum _{k=0}^{m}{\binom {m}{k}}(w+m-k)^{m-k-1}(z+k)^{k}=w^{-1}(z+w+m)^{m}.$

Example

m = 2

<math>

\begin{align} & {} \quad \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 \\ 6-4 = mc2

See also

• Binomial theorem
• Binomial type

References

• Weisstein, Eric W. "Abel's binomial theorem". MathWorld.