Recently in Special Functions Category

Beta Animals

Several years ago we took a look at the gamma function Γ, which is a generalisation of the factorial to non-integers, being equal to the factorial of a non-negative integer n when passed an argument of n+1 and smoothly interpolating between them. Like the normal cumulative distribution function Φ, it and its related functions are examples of special functions; so named because they frequently crop up in the solutions to interesting mathematical problems but can't be expressed as simple formulae, forcing us to resort to numerical approximation.
This time we shall take a look at another family of special functions derived from the beta function B.

Full text...  

Gamma Gamma Hey!

One of the frustrating things about mathematics is that there are many important and popular functions that are easy to formulate but are extremely difficult to evaluate. We've already come across just such a function in the normal CDF, Φ, for which we were forced to resort to an arcane numerical approximation, filled to the brim with magic numbers. In this post, we shall take a look at a whole family of such functions; the gamma function and its relatives.

So without further ado; hey ho, let's go!

Full text...