An inequality for the Dirichlet distribution (Q1086906)

The paper proves that the Dirichlet distribution function \[ D(x_ 1,x_ 2,...,x_ n;m_ 1,m_ 2,...,m_ n;m_{n+1})\geq \] \[ \frac{\Gamma (m_ 1+m_ 2+...+m_{n+1})}{\Gamma (m_ 1)\Gamma (m_ 2)...\Gamma (m_{n+1})}B(x_ 1;m_ 1;m_ 2+...+m_{n+1})\times \] \[ B(x_ 2;m_ 2;m_ 3+...+m_{n+1})...B(x_ n;m_ n;m_{n+1}) \] where \(B(x;u;v)=\int^{x}_{0}t^{u-1}(1-t)^{v-1}dt\).