A

David

Darling

beta function

The beta function is the function

 

B(m, n) = integral sign xm -1 (1 - x)n - 1 dx.

 

It can be defined in terms of the gamma function by

 

B(m, n) =

 

Γ(m) Γ(n)
____________
Γ(m + n)

 

Many integrals can be reduced to the evaluation of beta functions.