factorialx
Factorialx is a generalized factorial function parameterized by a base value x. For a nonnegative integer n, factorialx(n) is the product x(x+1)(x+2)…(x+n−1). Equivalently, factorialx(n) = Γ(n+x)/Γ(x), where Γ denotes the gamma function. This construction is commonly known in mathematics as the rising factorial (x)^{(n)} or the Pochhammer symbol (x)_{n}, and factorialx is a name used in some contexts for that quantity when x is fixed and n varies.
For an integer n ≥ 0, factorialx(0) = 1 and factorialx(n+1) = (x+n)·factorialx(n). The gamma-function expression provides a natural
Examples illustrate the concept: factorialx(5) with x = 3 equals 3·4·5·6·7 = 2520; factorialx(3) with x = 1.5 equals