On the asymptotic behaviour of analytic solutions of linear iterative functional equations

摘要

We obtain a representation for analytic solutions to linear iterative functional equations in a sectoral neighbourhood of a repelling fixed point of the iterated map. From this representation we deduce an asymptotic expansion of such solutions. Under some additional assumptions this expansion can be used to get the asymptotic behaviour of the power series coefficients of the solution. Finally examples from combinatorics and probability theory are provided.