B.16 GAMMA FUNCTIONS
Definition: Gamma Function The gamma function is the following definite integral:
(B.84) 
where 
(though we only consider real values in this book).
It has the following property: 
, and for 
:
For noninteger numbers a, the gamma function can be viewed as an extension of the factorial function. A plot of 
is provided in Figure B.11. Observe that for negative integers, the function alternates between 
, and for positive integers it is the factorial function (with argument shifted down by one), as given in (B.85). It can also be shown that for 
:
Figure B.11 Gamma function .
(B.86)
with and . The Euler–Masheroni constant (described later) is related to the gamma ...
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