DMTCS Proceedings, 2007 Conference on Analysis of Algorithms, AofA 07

A new method for computing asymptotics of diagonal coefficients of multivariate generating functions

Alexander Raichev, Mark C. Wilson

Abstract


Let
Σ
&nvec;∈&nats;
d
F
&nvec;
&xvec;
&nvec;
be a multivariate generating function that converges in a neighborhood of the origin of
&comps;
d
. We present a new, multivariate method for computing the asymptotics of the diagonal coefficients
F
a
1
n,…,a
d
n
and show its superiority over the standard, univariate diagonal method. Several examples are given in detail.

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