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), xPn, Px,n, or xPn. (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.
Read more about this topic: Pochhammer Symbol
Famous quotes containing the word alternate:
“Strange, that some of us, with quick alternate vision, see beyond our infatuations, and even while we rave on the heights, behold the wide plain where our persistent self pauses and awaits us.”
—George Eliot [Mary Ann (or Marian)