Asymptotic analysis of a class of functional equations and applications (Q1320521)

Motivated by some recent results of \textit{P. Flajolet} and \textit{B. Richmond} [Random Struct. Algorithms 3, No. 3, 305--320 (1992; Zbl 0758.60015)] the authors extend some results arising in the analysis of algorithms and exhibit some applications to stochastic processes related to average life problems. The key point of the paper is the detailed and ingenious study of the functional equation \(G(z) P_1(z) = G (\lambda z) P_2(z) + P_0 (z)\), where \(G\) is the unknown function and \(P_1\), \(P_2\), \(P_0\) are given polynomials. The asymptotic behaviour of a certain class of generating functions solutions of the above equation is made by means of the Mellin transform.