Mellin Transforms And Asymptotics: Harmonic Sums (1995)
| Venue: | Theoretical Computer Science |
| Citations: | 134 - 12 self |
BibTeX
@ARTICLE{Flajolet95mellintransforms,
author = {Philippe Flajolet and Xavier Gourdon and Philippe Dumas and Dedicated To Don Knuth and N. G. De Bruijn and Hjalmar Mellin},
title = {Mellin Transforms And Asymptotics: Harmonic Sums},
journal = {Theoretical Computer Science},
year = {1995},
volume = {144},
pages = {3--58}
}
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Abstract
. This survey presents a unified and essentially self-contained approach to the asymptotic analysis of a large class of sums that arise in combinatorial mathematics, discrete probabilistic models, and the average-case analysis of algorithms. It relies on the Mellin transform, a close relative of the integral transforms of Laplace and Fourier. The method applies to harmonic sums that are superpositions of rather arbitrary "harmonics" of a common base function. Its principle is a precise correspondence between individual terms in the asymptotic expansion of an original function and singularities of the transformed function. The main applications are in the area of digital data structures, probabilistic algorithms, and communication theory. Die Theorie der reziproken Funktionen und Integrale ist ein centrales Gebiet, welches manche anderen Gebiete der Analysis miteinander verbindet. --- Hjalmar Mellin Introduction Hjalmar Mellin (1854--1933, see [59] for a summary of his works) gave his ...
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