Pochhammer Symbol - Alternate Notations

Alternate Notations

A new notation was introduced by Ronald L. Graham, Donald E. Knuth and Oren Patashnik in their book Concrete Mathematics. They define, for the rising factorial:

and for the falling factorial:

they also propose to pronounce these expressions as "x to the m rising" and "x to the m falling", respectively.

Other notations for the falling factorial include P(x, n), xP_n, P_x,n, or _xP_n. (See permutation and combination.)

An alternate notation for the rising factorial x(n) is the less common (x)+_n. When the notation (x)+_n is used for the rising factorial, the notation (x)–_n is typically used for the ordinary falling factorial to avoid confusion.