B.22 RISING AND FALLING FACTORIALS
Definition: Rising and Falling Factorials The rising factorial is
(B.116)
for and . The falling factorial is
(B.117)
Except for x(0) = (x)0 = 1, these functions yield polynomials in x, such as
(B.118)
They are related as follows:
(B.119)
and have the following properties:
(B.120)
(B.121)
where is the gamma function and is a binomial coefficient. When :
(B.122)
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