beta

Dependents

this module uses 2 subunits Log_GammaMachine_Epsilon

Interface

Beta

This component evaluates the (complete) Beta integral with given parameters, defined by

The following properties also hold

As an illustration of the shape of this function, the following graph show the variation over a wide range of x, but small y:

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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