# Pochhammer symbol

In mathematics, the**Pochhammer symbol**

**"rising factorial"**or "upper factorial"

**"falling factorial"**or "lower factorial"

*x*)

_{0}is defined to be 1 in both cases.

The falling factorial occurs in a formula which represents polynomials using the forward difference operator Δ and which is formally similar to Taylor's theorem of calculus. In this formula and in many other places, the falling factorial (*x*)_{k} in the calculus of finite differences plays the role of *x*^{k} in differential calculus. Note for instance the similarity of

*D*denotes differentiation with respect to

*x*).

The notation was introduced by Leo August Pochhammer.

An alternative notation used by Ronald L. Graham, Donald E. Knuth and Oren Patashnik in their book *Concrete Mathematics* uses