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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 = 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.

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