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doc ///
Key
Beta
(Beta,CC,CC)
(Beta,CC,RR)
(Beta,RR,CC)
(Beta,RR,RR)
(Beta,RR,RRi)
(Beta,RRi,RR)
(Beta,RRi,RRi)
Headline
Beta function
Usage
Beta(x, y)
Inputs
x:RR
y:RR
Outputs
:RR -- the beta function of @TT "x"@ and @TT "y"@
Description
Text
This is the @wikipedia "beta function"@
\(B(x,y) = \int_0^1 t^{x - 1}(1 - t)^{y - 1}\,dt\).
Example
Beta(3, 4)
SeeAlso
regularizedBeta
inverseRegularizedBeta
///
doc ///
Key
regularizedBeta
(regularizedBeta,CC,CC,CC)
(regularizedBeta,CC,CC,RR)
(regularizedBeta,CC,RR,CC)
(regularizedBeta,CC,RR,RR)
(regularizedBeta,RR,CC,CC)
(regularizedBeta,RR,CC,RR)
(regularizedBeta,RR,RR,CC)
(regularizedBeta,RR,RR,RR)
(regularizedBeta,RR,RR,RRi)
(regularizedBeta,RR,RRi,RR)
(regularizedBeta,RR,RRi,RRi)
(regularizedBeta,RRi,RR,RR)
(regularizedBeta,RRi,RR,RRi)
(regularizedBeta,RRi,RRi,RR)
(regularizedBeta,RRi,RRi,RRi)
Headline
regularized beta function
Usage
regularizedBeta(x, a, b)
Inputs
x:RR
a:RR
b:RR
Outputs
:RR
Description
Text
This is the regularized (incomplete) @wikipedia "beta function"@
\(I_x(a, b) = \frac{1}{B(a, b)}\int_0^x t^{a - 1} (1 - t)^{b - 1}\,dt\).
Example
regularizedBeta(1/2, 3, 4)
1/Beta(3,4) * integrate(t -> t^2 * (1 - t)^3, 0, 1/2)
SeeAlso
Beta
inverseRegularizedBeta
///
doc ///
Key
inverseRegularizedBeta
(inverseRegularizedBeta,RR,RR,RR)
Headline
inverse of the regularized beta function
Usage
inverseRegularizedBeta(y, a, b)
Inputs
y:RR
a:RR
b:RR
Outputs
:RR
Description
Text
This is the inverse of @TO regularizedBeta@ with respect to the first
argument.
Example
regularizedBeta(1/2, 3, 4)
inverseRegularizedBeta(oo, 3, 4)
SeeAlso
Beta
regularizedBeta
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