Definition:Falling Factorial/Notation

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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 $\paren x_n$.

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

See the note on notation in the Rising Factorial entry.