This paper contains a parametric generalization of the classical
Poincare-Perron theorem and as its application a generalization of a known
theorem by Szego on the asymptotic ratio for sequence of polynomial orthogonal
on [-1,1] w.r.t. a non-negative weight satisfying some mild nongeneracy
assumptions. As a concrete application we calculate the asymptotic ratio for
sequences of biorthogonal polynomials of Ismail-Masson.