How does one interpret the subscript on a gamma function? For example, in the two parameter Gamma Cumulative Distribution Function:
What does the subscript mean in terms of how I should evaluate the gamma function.
I believe that denotes the incomplete gamma function.
There is no closed form expression for this guy as a function of . If you fix and try to write as a function of you can sometimes do that, particularly if is a positive integer.
You can but it probably will not be so useful for whatever you are doing. To take derivative wrt you may interchange integration and differentiation. So
To take derivative wrt you can use (chain rule + fundamental theorem of calculus). You can't get rid of the integrals though.