Safe Haskell | None |
---|---|

Language | Haskell2010 |

## 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