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We introduce poly-Bergman type spaces on the Siegel domain $D_nsubset mathbb{C}^n$, and we prove that they are isomorphic to tensorial products of one-dimensional spaces generated by orthogonal polynomials of two kinds: Laguerre polynomials and Hermite type polynomials. The linear span of all poly-Bergman type spaces is dense in the Hilbert space $L^2(D_n,dmu_{lambda})$, where $dmu_{lambda}=(im z_n - |z_1|^2-cdots -|z_{n-1}|^2)^{lambda}dx_1dy_1cdots dx_n dy_n$, with $lambda>-1$

Poly-Bergman Type Spaces on the Siegel Domain: Quasi-parabolic Case