Definition:Rising Factorial/Notation

Notation for Rising Factorial
The notation $x^{\overline k}$ for $x$ to the $k$ rising 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 $x^{\left({k}\right)}$.

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

However, depending on the context, either $\left({x}\right)_k$ or $x^{\left({k}\right)}$ can be used to indicate the rising factorial. In the field of combinatorics $x^{\left({k}\right)}$ tends to be used, while in that of special functions you tend to see $\left({x}\right)_k$. Therefore the more intuitively obvious $x^{\overline k}$ is becoming the preferred symbol for this.

See the note on notation in the Falling Factorial entry.