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