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.17 BETA FUNCTIONS
Definition: Beta Function The beta function is
(B.94) 
for a, b > 0.
The beta function is symmetric with respect to its parameters: B(a, b) = B(b, a), as illustrated in Figure B.14. The incomplete beta function is obtained by replacing the definite integral with an indefinite integral as follows:
Figure B.14 Beta function B(a, b).
(B.95) 
Obviously, B1(a, b) = B(a, b). Sometimes it is notationally convenient to use the regularized incomplete beta function:
(B.96) 
which is a normalized form (this notation should not be confused with the indicator function).
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