beta (MATLAB Functions)

MATLAB Function Reference

beta

Beta function

Syntax

```
B = beta(Z,W)
```

Definition

The beta function is

where is the gamma function.

Description

B = beta(Z,W) computes the beta function for corresponding elements of arrays Z and W. The arrays must be real and nonnegative. They must be the same size, or either can be scalar.

Examples

In this example, which uses integer arguments,

beta(n,3)
   = (n-1)!*2!/(n+2)!
   = 2/(n*(n+1)*(n+2))

is the ratio of fairly small integers, and the rational format is able to recover the exact result.

format rat 
beta((0:10)',3)

ans =

     1/0 
     1/3 
     1/12 
     1/30 
     1/60 
     1/105 
     1/168 
     1/252 
     1/360 
     1/495 
     1/660

Algorithm

beta(z,w) = exp(gammaln(z)+gammaln(w)-gammaln(z+w))

See Also

betainc, betaln, gammaln

bessely betainc