July 2020 Archives

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.

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