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5.8.16 The β function: Beta

The β function is defined by

β(x,y)=
1


0
tx−1 (1−t)y−1 =
Γ(x)*Γ(y)
Γ(x+y)

This is defined for x and y positive reals (to ensure the convergence of the integral) and by extension for x and y if they are not negative integers.
Remarkable values:

β(1,1)=1,   β(n,1)=
1
n
,   β(n,2)=
1
n(n+1)

The Beta command computes the β function.

Examples.


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