Definition:Rising Factorial/Notation

Notation for Rising Factorial
The notation $x^{\overline n}$ for $x$ to the $n$ 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 $x^{\paren n}$.

This is known as the Pochhammer function or (together with $\paren x_n$ for its falling counterpart) the Pochhammer symbol (after ).

However, depending on the context, either $\paren x_n$ or $x^{\paren n}$ can be used to indicate the rising factorial.

In the field of combinatorics $x^{\paren n}$ tends to be used, while in that of special functions you tend to see $\paren x_n$.

Therefore the more intuitively obvious $x^{\overline n}$ is becoming the preferred symbol for this.

See the note on notation in the Falling Factorial entry.