# 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

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

$"{displaystyle$

Índice

## Example[]

### The case m = 2[]

$"{displaystyle$

( 2 0 ) ( w + 2 ) 1 ( z + 0 ) 0 + ( 2 1 ) ( w + 1 ) 0 ( z + 1 ) 1 + ( 2 2 ) ( w + 0 ) 1 ( z + 2 ) 2 = ( w + 2 ) + 2 ( z + 1 ) + ( z + 2 ) 2 w = ( z + w + 2 ) 2 w . {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}}}