Descriptions of the models are given starting in Section A.2. First, a few mathematical preliminaries are presented that indicate how the various quantities can be computed.
The incomplete gamma function1 is given by
A useful fact is . Also, define
At times, we will need this integral for nonpositive values of . Integration by parts produces the relationship
This process can be repeated until the first argument of G is , a positive number. Then, it can be evaluated from
However, if is a negative integer ...