Abel's binomial theorem

Abel's binomial theorem, named after Niels Henrik Abel, is a mathematical identity involving sums of binomial coefficients. It states the following:

Abel's binomial theorem, named after Niels Henrik Abel, is a mathematical identity involving sums of binomial coefficients. It states the following:

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

Índice

Example[]

{displaystyle {begin{aligned}&{}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}\&=(w+2)+2(z+1)+{frac {(z+2)^{2}}{w}}\&={frac {(z+w+2)^{2}}{w}}.end{aligned}}}

This number theory-related article is a stub. You can help Wikipedia by expanding it.

Hidden categories:

Si quieres conocer otros artículos parecidos a Abel's binomial theorem puedes visitar la categoría Factorial and binomial topics.