Abstract
An asymptotic formula is given for the solutions of a linear second-order difference equation which holds in the case that the coefficients exhibit regular behaviour; in particular, the formula holds in the case that the coefficients are series of powers of the index n. The lowest order asymptotic behaviour is given for both x
n
and
. Examples are given that show that the conditions on the behaviour of the coefficients cannot be weakened too much. The method presented here, which uses matrix sequences, can be extended to other cases.