Gyan: Created page with 'The beta function is defined by: $\Beta(m,n)=\int_0^1 x^{m-1}(1-x)^{n-1}dx$ in scilab beta(m,n) evaluates the beta function at all the elements of m and n. e.g. …'

2012-12-24T10:43:15Z

Created page with '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. …'

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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

Beta function - Revision history

Gyan: Created page with 'The beta function is defined by: \Beta(m,n)=\int_0^1 x^{m-1}(1-x)^{n-1}dx in scilab beta(m,n) evaluates the beta function at all the elements of m and n. e.g. …'

Gyan: Created page with 'The beta function is defined by: $\Beta(m,n)=\int_0^1 x^{m-1}(1-x)^{n-1}dx$ in scilab beta(m,n) evaluates the beta function at all the elements of m and n. e.g. …'