Divide-and-Conquer Recurrences, Functional Equations and Their Asymptotic Analysis

Abstract

Introduction and formulation of main results There are several important problems, stemming from the theory of algorithms, probability theory etc., leading to the study of the asymptotic behaviour of the sequence ff n g defined by means of the recurrence relation [2 n \Gamma (a 1 + a 0 )]f n = a 1 n\Gamma1 X k=0 ` n k ' ff n\Gammak f k + b 1 fi n ; n ? l; (1.1) supplemented by given initial values f 0 ; f 1 ; : : : ; f l : (1.2) Here ff; fi ? 0, a 0 ; a 1 ; b 1 2 R are given parameters. Suppose