Math.SpecialFunction

Documentation

incbeta

Arguments

:: (Floating a, Ord a)

=> a

\(z\)

-> a

\(a\)

-> a

\(b\)

-> a

Incomplete beta function, \(|z|\leq 1\)

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

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

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

Since: 0.1.1.0

regbeta

Arguments

:: (Floating a, Ord a)

=> a

\(z\)

-> a

\(a\)

-> a

\(b\)

-> a

Regularized beta function, \(|z|\leq 1\)

\(I(z;a,b) = \displaystyle\frac{B(z;a,b)}{B(a,b)}\)

bessel1

Arguments

:: (Floating a, Ord a)

=> a

\(\alpha\)

-> a

\(x\)

-> a

Bessel functions of the first kind, \( J_\alpha(x)\).

Since: 0.1.3.0

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

\(\Gamma(z)\)

Since: 0.1.1.0

gammaln

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

agm :: (Ord a, Floating a) => a -> a -> a

Arithmetic-geometric mean

Since: 0.1.4.0

completeElliptic :: (Ord a, Floating a) => a -> a

Complete elliptic integral of the first kind

Since: 0.1.4.0

fcdf

Arguments

:: (Floating a, Ord a)

=> a

\(n\)

-> a

\(m\)

-> a

\(x\)

-> a

Since: 0.1.2.0

chisqcdf

Arguments

:: (Floating a, Ord a)

=> a

\(r\) (degrees of freedom)

-> a

\(\chi^2\)

-> a

Since: 0.1.2.0

tcdf

Arguments

:: (Floating a, Ord a)

=> a

\(\nu\) (degrees of freedom)

-> a

\(x\)

-> a

Converges if and only if \(|x| \leq \sqrt{\nu} \)

Since: 0.1.2.0