Abstract:
A Riordan array is an infinite complex matrix (ars) of a certain type (see below for
exact definitions). The Riordan array formalism has been much used recently to study
combinatorial questions in analysis of algorithms and other areas. Most work has been
concerned with “exact” results. In this article we discuss asymptotics of such arrays.
We apply general machinery for deriving asymptotics of bivariate generating functions,
following the research programme begun in [PW02, PW04]. Asymptotic expansions of special
cases of Riordan arrays have been discussed by several authors [Drm94, Gar95]. The
main purposes of this article are to show how the work in [PW02] immediately yields strong
results for (a generalization of) Riordan arrays, and to use this case as an introduction to the
much more general results in [PW02, PW04], the computations being simpler to understand.
In addition we try to simplify and automate the process of extracting asymptotics as far as
possible.