The rising factorial x^(n), sometimes also denoted 〈x〉_n or x^(n^_) , is defined by x^(n) = x(x + 1)...(x + n - 1). This function is also known as the rising factorial power and frequently called the Pochhammer symbol in the theory of special functions. The rising factorial is implemented in the Wolfram Language as Pochhammer[x, n]. The rising factorial is related to the gamma function Γ(z) by x^(n) congruent (Γ(x + n))/(Γ(x)), where x^(0) congruent 1, and is related to the falling factorial (x)_n by x^(n) = (-x)_n (-1)^n.

central factorial | factorial | falling factorial | gamma function | generalized hypergeometric function | harmonic logarithm | hypergeometric function | Pochhammer symbol