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:
“In museums and palaces we are alternate radicals and conservatives.”
—Henry James (1843–1816)