Asymptotic analysis of a class of functional equations and applications
Journal de théorie des nombres de Bordeaux, Volume 5 (1993) no. 2, pp. 365-381.

Flajolet and Richmond have invented a method to solve a large class of divide-and-conquer recursions. The essential part of it is the asymptotic analysis of a certain generating function for $z\to \infty$ by means of the Mellin transform. In this paper this type of analysis is performed for a reasonably large class of generating functions fulfilling a functional equation with polynomial coefficients. As an application, the average life time of a party of $N$ people is computed, where each person advances one step or dies with equal probabilities, and an additional “killer” can kill at any level up to $d$ survivors, according to his probability distribution.

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author = {Grabner, P. J. and Prodinger, H. and Tichy, R. F.},
title = {Asymptotic analysis of a class of functional equations and applications},
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Grabner, P. J.; Prodinger, H.; Tichy, R. F. Asymptotic analysis of a class of functional equations and applications. Journal de théorie des nombres de Bordeaux, Volume 5 (1993) no. 2, pp. 365-381. http://www.numdam.org/item/JTNB_1993__5_2_365_0/

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