gamma-0.10.0.0: Gamma function and related functions.

Math.Gamma.Incomplete

Synopsis

# Documentation

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

Continued fraction representation of the lower incomplete gamma function.

pCF :: (Gamma a, Ord a, Enum a) => a -> a -> CF a Source #

Continued fraction representation of the regularized lower incomplete gamma function.

lowerGammaHypGeom :: (Eq b, Floating b) => b -> b -> b Source #

Lower incomplete gamma function, computed using Kummer's confluent hypergeometric function M(a;b;x). Specifically, this uses the identity:

gamma(s,x) = x**s * exp (-x) / s * M(1; 1+s; x)

From Abramowitz & Stegun (6.5.12).

Recommended for use when x < s+1

lnLowerGammaHypGeom :: (Eq a, Floating a) => a -> a -> a Source #

Natural logarithm of lower gamma function, based on the same identity as lowerGammaHypGeom and evaluated carefully to avoid overflow and underflow. Recommended for use when x < s+1

pHypGeom :: (Gamma a, Ord a) => a -> a -> a Source #

Regularized lower incomplete gamma function, computed using Kummer's confluent hypergeometric function. Uses same identity as lowerGammaHypGeom.

Recommended for use when x < s+1

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

Continued fraction representation of the upper incomplete gamma function. Recommended for use when x >= s+1

lnUpperGammaConvergents :: (Eq a, Floating a) => a -> a -> [a] Source #

Natural logarithms of the convergents of the upper gamma function, evaluated carefully to avoid overflow and underflow. Recommended for use when x >= s+1

qCF :: (Gamma a, Ord a, Enum a) => a -> a -> CF a Source #

Continued fraction representation of the regularized upper incomplete gamma function. Recommended for use when x >= s+1