  The discrete group generated by reflections of the sphere, or Euclidean
space, or hyperbolic space are said to be Coxeter groups of, respectively,
spherical, or Euclidean, or hyperbolic type. The hyperbolic Coxeter groups are
said to be (quasi-)Lann\'er if the tiles covering the space are of finite
volume and all (resp. some of them) are compact. For any Coxeter group
stratified by the length of its elements, the Poincar\'e series (a.k.a. growth
function) is the generating function of the cardinalities of sets of elements
of equal length. Solomon established that, for ANY Coxeter group, its
Poincar\'e series is a rational function with zeros somewhere on the unit
circle centered at the origin, and gave a recurrence formula. The explicit
expression of the Poincar\'e series was known for the spherical and Euclidean
Coxeter groups, and 3-generated Coxeter groups, and (with mistakes) Lann\'er
groups. Here we give a lucid description of the numerator of the Poincar\'e
series of any Coxeter group, and denominators for each (quasi-)Lann\'er group,
and review the scene. We give an interpretation of some coefficients of the
denominator of the Poincar\'e series. The non-real poles behave as in
Enestr\"om's theorem (lie in a narrow annulus) though the coefficients of the
denominators do not satisfy theorem's requirements.
