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

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

2007-02-20

arxiv.org/abs/math/0702595v1

Mathematics

Combinatorics

9 pages, no figures

Scientific paper

Let \sum_{n\in N^d} f_{n_1, ..., n_d} x_1^{n_1}... x_d^{n_d} be a
multivariate generating function that converges in a neighborhood of the origin
of C^d. We present a new, multivariate method for computing the asymptotics of
the diagonal coefficients f_{a_1n,...,a_dn} and show its superiority over the
standard, univariate diagonal method.

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