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doc ///
Key
Gamma
(Gamma,CC)
(Gamma,CC,CC)
(Gamma,CC,RR)
(Gamma,RR)
(Gamma,RR,CC)
(Gamma,RR,RR)
(Gamma,RR,RRi)
(Gamma,RRi)
(Gamma,RRi,RR)
(Gamma,RRi,RRi)
Headline
Gamma function
Usage
Gamma x
Gamma(s, x)
Inputs
s:RR
x:RR
Outputs
:RR
Description
Text
With one argument, this is the @wikipedia "gamma function"@
\(\Gamma(x) = \int_0^\infty t^{x-1}e^{-t}\,dt\).
Example
Gamma 6
Text
With two arguments, it is the (upper)
@wikipedia "incomplete gamma function"@
\(\Gamma(s, x) = \int_x^\infty t^{s-1}e^{-t}\,dt\).
Example
Gamma(3, 7)
SeeAlso
regularizedGamma
inverseRegularizedGamma
///
doc ///
Key
regularizedGamma
(regularizedGamma,CC,CC)
(regularizedGamma,CC,RR)
(regularizedGamma,RR,CC)
(regularizedGamma,RR,RR)
(regularizedGamma,RR,RRi)
(regularizedGamma,RRi,RR)
(regularizedGamma,RRi,RRi)
Headline
upper regularized gamma function
Usage
regularizedGamma(s, x)
Inputs
s:RR
x:RR
Outputs
:RR
Description
Text
This is the (upper) regularized gamma function
\(Q(s, x) = \frac{\Gamma(s,x)}{\Gamma(s)}\).
Example
regularizedGamma(3, 7)
Gamma(3, 7) / Gamma 3
SeeAlso
Gamma
inverseRegularizedGamma
///
doc ///
Key
inverseRegularizedGamma
(inverseRegularizedGamma,RR,RR)
Headline
inverse of the upper regularized gamma function
Usage
inverseRegularizedGamma(s, q)
Inputs
s:RR
q:RR
Outputs
:RR
Description
Text
This is the inverse of @TO regularizedGamma@ with respect to the second
argument.
Example
regularizedGamma(3, 7)
inverseRegularizedGamma(3, oo)
SeeAlso
Gamma
regularizedGamma
///
doc ///
Key
lngamma
(lngamma, RR)
(lngamma, CC)
(lngamma, RRi)
(lngamma, Number)
Headline
logarithm of the Gamma function
Usage
lngamma x
Inputs
x:RR
Outputs
:{RR, CC}
the logarithm of the @TO Gamma@ function of @TT "x"@ as a real
or complex number.
Description
Example
lngamma 2.1
lngamma(-1.1)
lngamma(-2.1)
lngamma (-2.000000000000000000000000000000001p120)
SeeAlso
Gamma
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