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beta

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Evaluates the Beta function.
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Contents

C++

Beta

 doublebeta( double x double y )
This component evaluates the (complete) Beta integral with given parameters, defined by
$B(x,&space;y)&space;=&space;\frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}$

The following properties also hold

$B(x,&space;y)&space;=&space;B(y,&space;x)&space;\qquad&space;&space;B(x,&space;y)&space;=&space;\int_0^1&space;t^{x-1}&space;(1-t)^{y-1}&space;\mathrm{d}t$

As an illustration of the shape of this function, the following graph show the variation over a wide range of x, but small y:
There is an error with your graph parameters for beta with options x=0.2:10 y=0.1:0.5:5 .size=medium

Error Message:Function beta failed. Ensure that: Invalid C++

Example 1

#include <codecogs/maths/special/gamma/beta.h>
#include <iostream>
#include <iomanip>

int main()
{
std::cout << std::setprecision(10);
for (double x = 3; x < 5; x += 0.2)
{
std::cout << "Beta(" << x << ", 3.3) = ";
std::cout << Maths::Special::Gamma::beta(x, 3.3) << std::endl;
}
return 0;
}
Output:
Beta(3, 3.3) = 0.02659326924
Beta(3.2, 3.3) = 0.02259427655
Beta(3.4, 3.3) = 0.01935107719
Beta(3.6, 3.3) = 0.01669372181
Beta(3.8, 3.3) = 0.0144961426
Beta(4, 3.3) = 0.01266346154
Beta(4.2, 3.3) = 0.01112333615
Beta(4.4, 3.3) = 0.00981994962
Beta(4.6, 3.3) = 0.008709767899
Beta(4.8, 3.3) = 0.007758498858

References

John Burkardt's library of statistical C++ routines, http://www.csit.fsu.edu/~burkardt/cpp_src/prob/prob.html

Parameters

 x the first argument of the function. Must be positive (x>0). y the second argument of the function. Must be positive (x>0).

Returns

An approximation of the Beta function

Authors

Lucian Bentea (September 2005)
Source Code

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