beta function

The function

B(m, n) =

x^{m -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.

Related category

• FUNCTIONS

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