Definition:Falling Factorial/Notation

From ProofWiki
Jump to navigation Jump to search

Notation for Falling Factorial

The notation $x^{\underline n}$ for $x$ to the $n$ falling is due to Alfredo Capelli, who used it in $1893$.

This is the notation of choice on $\mathsf{Pr} \infty \mathsf{fWiki}$.


A more commonly seen notation (though arguably not as good) is $\left({x}\right)_n$.

This is known as the Pochhammer function or (together with $x^{\left({n}\right)}$ for its rising counterpart) the Pochhammer symbol (after Leo August Pochhammer).


See the note on notation in the Rising Factorial entry.


Sources