Asymptotic analysis of solutions of differential equations with polynomially periodic coefficients

From the text (translated from the Russian): "We consider a system of nonautonomous differential equations with polynomial coefficients of the form gathered dot x=bigg(sum^{infty}_{k=0}A_k(t)t^{m-k}bigg) x,quad tgeq t_0>1, x(t_0)=x^0, endgathered where mgeq -1, xin{bf R}^n and the A_k(cdot) (kgeq 0) are sufficiently smooth ntimes n matrix functions that are T-periodic on the semiaxis [t_0,+infty). Our results supplement those of W. Wasow [{it Asymptotic expansions for ordinary differential equations}, Interscience Publishers John Wiley & Sons, Inc., New York, 1965; [msn] MR0203188 (34 #3041) [/msn]], B. P. Demidovich [{it Lectures on the mathematical theory of stability} (Russian), Izdat. "Nauka", Moscow, 1967; [msn] MR0226126 (37 #1716) [/msn]], and A. F. Nikiforov and V. B. Uvarov [{it Foundations of the theory of special functions} (Russian), Izdat. "Nauka", Moscow, 1974; [msn] MR0460737 (57 #730) [/msn]]. One can reduce the hypergeometric equation p(t)ddot x+q(t)dot x+lambda x=0, where q(t) and p(t) are polynomials whose degrees are not greater than one or two, respectively, lambda is a constant parameter, and their special cases the equations of Airy, Bessel, Hermite, and many others to the above-mentioned system (for constant A_k)."