Definition:Falling Factorial/Notation

Notation for Falling Factorial
The notation $x^{\underline k}$ for $x$ to the $k$ falling is due to, who used it in $1893$.

This is the notation of choice on.

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

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

See the note on notation in the Rising Factorial entry.