beta — Math

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beta( z, w )

The beta function of z and w in Math, is special function. Defined by

$\operatorname{B} (z,w) = \int_0^1 \; t^{z-1} (1-t)^{w-1} \ dt$

beta(a,b) = beta(b,a)

beta(1,x) = beta(x,1) = 1/x
beta(1,1) = 1

beta( x, y, z ) — incomplete beta function of real or complex numbers, where x = 1 replicates the beta function.
beta(1,y,z) = beta(y,z)

Relation to gamma:

$\operatorname{B} (z,w) = \frac{ \Gamma(z) \Gamma(w) }{ \Gamma(z+w) }$

Real part on the real space:
beta(x,y)

Real part on the real plane:

Related functions: gamma

Function category: gamma functions