  In a previous paper (Radial operators on polyanalytic weighted Bergman
spaces, Bol. Soc. Mat. Mex. 27, 43), using disk polynomials as an orthonormal
basis in the $n$-analytic weighted Bergman space, we showed that for every
bounded radial generating symbol $a$, the associated Toeplitz operator, acting
in this space, can be identified with a matrix sequence $\gamma(a)$, where the
entries of the matrices are certain integrals involving $a$ and Jacobi
polynomials. In this paper, we suppose that the generating symbols $a$ have
finite limits on the boundary and prove that the C*-algebra generated by the
corresponding matrix sequences $\gamma(a)$ is the C*-algebra of all matrix
sequences having scalar limits at infinity. We use Kaplansky's noncommutative
analog of the Stone--Weierstrass theorem and some ideas from several papers by
Loaiza, Lozano, Ram\'{i}rez-Ortega, Ram\'{i}rez-Mora, and S\'{a}nchez-Nungaray.
We also prove that for $n\ge 2$, the closure of the set of matrix sequences
$\gamma(a)$ is not equal to the generated C*-algebra.
