November 2012
Intermediate to advanced
794 pages
22h 9m
English
book
Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
by John J. Shynk
Content preview from Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
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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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