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The Selberg integral has a twin (`the Dotsenko--Fateev integral') of thefollowing 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 Selbergintegral by complex variables $z_k$, integration over a cube we replace by anintegration over the whole complex space $\mathbb{C}^n$. According to Dotsenko,Fateev, and Aomoto, such integral is a product of Gamma functions. We defineand 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 thecomplex twin of the Selberg integral mentioned above (with three additionalinteger parameters)

On the Dotsenko-Fateev complex twin of the Selberg integral and its extensions