Safe Haskell	Safe-Inferred
Language	Haskell2010

Math.SpecialFunction

Synopsis

incbeta :: (Floating a, Eq a) => a -> a -> a -> a
beta :: (Floating a, Ord a) => a -> a -> a
gamma :: (Floating a, Ord a) => a -> a
gammaln :: (Floating a, Ord a) => a -> a

Documentation

incbeta Source #

Arguments

:: (Floating a, Eq a)
=> a	\(z\)
-> a	\(a\)
-> a	\(b\)
-> a

Incomplete beta function.

Calculated with \(B(z;a,b)=\displaystyle\frac{z^a}{a}{}_2F_1(a, 1-b; a+1; z)\)

Since: 0.1.1.0

beta :: (Floating a, Ord a) => a -> a -> a Source #

\(B(x, y) = \displaystyle\frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\)

This uses gammaln under the hood to extend its domain somewhat.

Since: 0.1.1.0

gamma :: (Floating a, Ord a) => a -> a Source #

\(\Gamma(z)\)

Since: 0.1.1.0

gammaln Source #

Arguments

:: (Floating a, Ord a)
=> a	\( z \)
-> a

\(\text{log} (\Gamma(z))\)

Lanczos approximation. This is exactly the approach described in Press, William H. et al. Numerical Recipes, 3rd ed., extended to work on negative real numbers.

Since: 0.1.1.0