Incomplete Beta Function
المؤلف:
Pearson, K.
المصدر:
Tables of Incomplete Beta Functions, 2nd ed. Cambridge, England: Cambridge University Press, 1968.
الجزء والصفحة:
...
22-5-2019
1954
Incomplete Beta Function
A generalization of the complete beta function defined by
 |
(1)
|
sometimes also denoted 
. The so-called Chebyshev integral is given by
 |
(2)
|
The incomplete beta function is implemented in the Wolfram Language as Beta[z, a, b].
It is given in terms of hypergeometric functions by
It is also given by the series
 |
(5)
|
where 
is a Pochhammer symbol.
The incomplete beta function 
reduces to the usual beta function 
when 
,
 |
(6)
|
It has derivative
 |
(7)
|
and indefinite integral
 |
(8)
|
REFERENCES:
Pearson, K. (Ed.). Tables of Incomplete Beta Functions, 2nd ed. Cambridge, England: Cambridge University Press, 1968.
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