en>Cydebot: Robot - Speedily moving category Acid-base chemistry to :Category:Acid–base chemistry per CFDS.

2014-08-05T23:57:33Z

Robot - Speedily moving category Acid-base chemistry to Category:Acid–base chemistry per CFDS.

en>ClueBot NG: Reverting possible vandalism by 86.132.115.169 to version by Gabriel Kielland. False positive? Report it. Thanks, ClueBot NG. (672755) (Bot)

2011-10-23T18:47:42Z

Reverting possible vandalism by 86.132.115.169 to version by Gabriel Kielland. False positive? Report it. Thanks, ClueBot NG. (672755) (Bot)

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

: <math>\sum_{k=0}^m \binom{m}{k} (w+m-k)^{m-k-1}(z+k)^k=w^{-1}(z+w+m)^m.</math>

==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 \\
& = (w+2)+2(z+1)+\frac{(z+2)^2}{w} \\
& = \frac{(z+w+2)^2}{w}.
\end{align}
</math>

==See also==

* [[Binomial theorem]]
* [[Binomial type]]

==References==

* {{mathworld|title=Abel's binomial theorem|urlname=AbelsBinomialTheorem}}

[[Category:Factorial and binomial topics]]
[[Category:Theorems in algebra]]

Acid neutralizing capacity - Revision history

en>Cydebot: Robot - Speedily moving category Acid-base chemistry to :Category:Acid–base chemistry per CFDS.

en>ClueBot NG: Reverting possible vandalism by 86.132.115.169 to version by Gabriel Kielland. False positive? Report it. Thanks, ClueBot NG. (672755) (Bot)