Difference between revisions of "Beta function"

Latest revision as of 16:13, 24 December 2012

The beta function is defined by:

<math>\Beta(m,n)=\int_0^1 x^{m-1}(1-x)^{n-1}dx</math>

in scilab beta(m,n) evaluates the beta function at all the elements of m and n.

e.g.

 -->beta(2,5)
  ans  =

     0.0333333

For the beta function

<math>\Beta(m,n)=\Beta(n,m)</math>

e.g.

 -->beta(2,5)
  ans  =

     0.0333333  

 -->beta(5,2)
  ans  =

     0.0333333

Also

<math>\Beta(m,n)=\frac{\Gamma(m)\Gamma(n)}{\Gamma(m+n)}</math>

which is a relation between beta and gamma function and can be verify by using the example given below:

e.g. Recall

 -->beta(2,5)
    ans  =

       0.0333333

and

 -->gamma(2)
  ans  =

     1.  

 -->gamma(5)
  ans  =

     24.  

 -->gamma(7)
  ans  =

     720.  

 -->1*24/720
  ans  =

     0.0333333  

that is

<math>\Beta(2,5)=\frac{\Gamma(2)\Gamma(5)}{\Gamma(2+5)}</math>

also,

 -->beta(1/2,1/2)
  ans  =

     3.1415927

and

 -->(gamma(1/2)*gamma(1/2))/gamma(1)
  ans  =

     3.1415927