I would like to have a tool for partial fraction expansion of polynomial quotient $ $ \frac{P(z)}{Q(z)},$ $ where the order of the polynomial $ P(z)$ is less than that of $ Q(z)$ .

The output of the function is expected to be the coefficients $ c_{ij}$ of the expansion: $ $ \sum_i\sum_{j=1}^{m_i}\frac{c_{ij}}{(z-\zeta_i)^j}, $ $ where the sum runs over all distinct roots $ \zeta_i$ (with multiplicity $ m_i$ ) of the polynomial $ Q(z)$ .

Is there a built-in function in Mathematica which is suitable for performing the task? For a symbolic computation the list of roots of the polynomial $ Q(z)$ can be supplied.