rising factorial power | rising power | shifted factorial

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].

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