7.13 The Pochhammer Notation

The Pochhammer notation (a)k (also called Pochhammer’s symbol) is supported by the binary operator POCHHAMMER(A,K). For a non-negative integer k, it is defined as (

(a)0 = 1,
(a)k = a(a + 1)(a + 2)⋅⋅⋅(a + k - 1).
For a = 0,1,2,, this is equivalent to
(a)k = Γ (a+-k-)
 Γ (a)
With ROUNDED off, this expression is evaluated numerically if a and k are both integral, and otherwise may be simplified where appropriate. The simplification rules are based upon algorithms supplied by Wolfram Koepf.