  Poincare polinomials of hyperbolic Lie algebras, which are given by $HA_2$
and $HA_3$ in the Kac's notation, are calculated explicitly. The results show
that there is a significant form for hyperbolic Poincare polinomials. Their
explicit forms tend to be seen as the ratio of a properly chosen finite
Poincare polinomial and a polinomial of finite degree. To this end, by choosing
the Poincare polinomials of $D_4$ and $D_5$ Lie algebras, we show that these
polinomials come out to be of order 11 and 19 respectively for $HA_2$ and
$HA_3$.
