| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Math.Gamma.Incomplete
Synopsis
- lowerGammaCF :: (Floating a, Ord a) => a -> a -> CF a
- pCF :: (Gamma a, Ord a, Enum a) => a -> a -> CF a
- lowerGammaHypGeom :: (Eq b, Floating b) => b -> b -> b
- lnLowerGammaHypGeom :: (Eq a, Floating a) => a -> a -> a
- pHypGeom :: (Gamma a, Ord a) => a -> a -> a
- upperGammaCF :: (Floating a, Ord a) => a -> a -> CF a
- lnUpperGammaConvergents :: (Eq a, Floating a) => a -> a -> [a]
- qCF :: (Gamma a, Ord a, Enum a) => a -> a -> CF a
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