The gamma function
The gamma function is a logarithmic, convex, smooth function operating on complex numbers, which interpolates the factorial function for all nonnegative integers. It is not defined at zero or any negative integer. This is the most common special function and is widely used in many different applications, either by itself or as the main ingredient in the definition of many other functions. The gamma function is used in diverse fields such as quantum physics, astrophysics, statistics, and fluid dynamics.
The gamma function is defined by the improper integral, as follows:
Evaluation of gamma at integer values gives shifted factorials, and that is precisely how the factorials are coded in SciPy.
The scipy.special module has algorithms to obtain a fast evaluation of the gamma function at any permissible value. It also contains routines to perform evaluation of the most common compositions of the gamma functions appearing in the literature: gammaln for the natural logarithm of...
