beta

Beta function

Syntax

B = beta(Z,W)


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 

More About

Beta Function

The beta function is

$$B(z,w)={{\displaystyle \int }}_0^1{t}^{z-1}{(1-t)}^{w-1}dt=\frac{\Gamma (z)\Gamma (w)}{\Gamma (z+w)}$$

where Γ(z) is the gamma function.

Algorithms

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

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

This function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).