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
 |  |  | (3) |
 |  |  | (4) |
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) |
 | (8) |
