The complete gamma function is a bit more difficult to implement than the incomplete gamma function. There are a number of different approximations. For more information, visit http://dlmf.nist.gov/5. There's a version available in the Python math library. It represents a broadly useful approximation that is designed for many situations.
We're not interested in a completely general implementation of the complete gamma function. We're interested in just two special cases: integer values and halves. For these two special cases, we can get exact answers, and don't need to rely on an approximation.
For integer values, . The complete gamma function for integers can rely on the factorial function we defined ...
