1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
|
doc ///
Key
Beta
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
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
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
///
|
