  Let $\Delta$ be a finite set of nonzero linear forms in several variables
with coefficients in a field $\mathbf K$ of characteristic zero. Consider the
$\mathbf K$-algebra $R(\Delta)$ of rational functions on V which are regular
outside $\bigcup_{\alpha\in\Delta} \ker\alpha$. Then the ring $R(\Delta)$ is
naturally doubly filtered by the degrees of denominators and of numerators. In
this paper we give an explicit combinatorial formula for the Poincar\'e series
in two variables of the associated bigraded vector space $\bar{R}(\Delta)$.
This generalizes the main theorem of Terao, H.: Algebras generated by
reciprocals of linear forms, to appear in J.Algebra (arXiv:math.CO/0105095).
