The Pochhammer Notation
Date: 2020-10-07 18:10:00

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### 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 (http://dlmf.nist.gov/5.2.iii)

(a)0 | = 1, |  |
(a)k | = a(a + 1)(a + 2)⋯(a + k − 1). |  |
For a≠0,±1,±2,…, this is equivalent to
(a)k | = |  |

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.

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