binomial polynomial | falling factorial power | falling power | lower factorial

The falling factorial (x)_n, sometimes also denoted x^(n__) , is defined by (x)_n = x(x - 1)...(x - (n - 1)) for n>=0. Is also known as the binomial polynomial, lower factorial, falling factorial power , or factorial power. The falling factorial is related to the rising factorial x^(n) (a.k.a. Pochhammer symbol) by (x)_n = (-1)^n (-x)^(n), The falling factorial is implemented in the Wolfram Language as FactorialPower[x, n].

binomial theorem | central factorial | Chu-Vandermonde identity | Pochhammer symbol | rising factorial | Sheffer sequence | sigma polynomial