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beta

Beta function

Syntax

B = beta(Z,W)

Definitions

The beta function is

B(z,w)=01tz1(1t)w1dt=Γ(z)Γ(w)Γ(z+w)

where Γ(z) 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 

More About

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Algorithms

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

See Also

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Introduced before R2006a

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