  The Selberg integral has a twin (`the Dotsenko--Fateev integral') of the
following form. We replace real variables $x_k$ in the integrand $\prod
|x_k|^{\sigma-1}\,|1-x_k|^{\tau-1} \prod|x_k-x_l|^{2\theta}$ of the Selberg
integral by complex variables $z_k$, integration over a cube we replace by an
integration over the whole complex space $\mathbb{C}^n$. According to Dotsenko,
Fateev, and Aomoto, such integral is a product of Gamma functions. We define
and evaluate a family of beta integrals over spaces $\mathbb{C}^m\times
\mathbb{C}^{m+1}\times \dots \times \mathbb{C}^n$, which for $m=n$ gives the
complex twin of the Selberg integral mentioned above (with three additional
integer parameters)
