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Asymptotics of coefficients of multivari...
Raichev, Alexander...

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Asymptotics of coefficients of multivariate generating functions: improvements for smooth points by Raichev, Alexander ( Author )
Lemonjar Open Access
N.A
20-03-2008
Let $\sum_{\beta\in\nats^d} F_\beta x^\beta$ be a multivariate power series. For example ∑Fβxβ could be a generating function for a combinatorial class. Assume that in a neighbourhood of the origin this series represents a nonentire function F=G/Hp where G and H are holomorphic and p is a positive integer. Given a direction $\alpha\in\pnats^d$ for which the asymptotics are controlled by a smooth point of the singular variety H=0, we compute the asymptotics of Fnα as n→∞. We do this via multivariate singularity analysis and give an explicit formula for the full asymptotic expansion. This improves on earlier work of R. Pemantle and the second author and allows for more accurate numerical approximation, as demonstrated by our examples.
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MYR 0.00
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https://arxiv.org/abs/0803.2914
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