Philippe Flajolet and Andrew Odlyzko developed singularity analysis as
``a class of methods by which one can translate, on a term-by-term
basis, an asymptotic expansion of a function around a dominant
singularity into a corresponding asymptotic expansion for the Taylor
coefficients of the function.'' I will discuss results that extend
this class, primarily the determination of how singularities get
composed under the Hadamard product of series, defined as
I will show how these results can be used to analyze asymptotically
recurrences arising in various settings including the random
permutation and uniform model on binary search trees and the evolution
of random graphs.
Singularity analysis and asymptotics of Bernoulli sums.
Theoret. Comput. Sci., 215(1-2):371-381, 1999.
Philippe Flajolet and Andrew Odlyzko.
Singularity analysis of generating functions.
SIAM J. Discrete Math., 3(2):216-240, 1990.
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