  For Poincare series of binary polyhedral groups and Coxeter polynomials there
are obtained statements close to the Euclid algorithm and orthogonal
polynomials theory: generalized Ebeling formula, decompositions into ramified
continued fractions, Christoffel-Darboux identity, combinatorial formula. Known
results about the factorization of the Alexander-Conway polynomial permit to
connect Poincare series and Coxeter polynomials with the Burau representation
and Milnor invariants of string links. One uses reconstractions of A'Campo
links and Coxeter links. There is formulated a conjecture connecting obtained
formulae with Poincare series of ring of functions on singularities through
results of S. M. Gusein-Zade, F. Delgado, and A. Campillo.
