@article{raichev2008asymptotics,
  title={Asymptotics of coefficients of multivariate generating functions: improvements for smooth points},
  author={Raichev, Alexander and Wilson, Mark C.},
  journal={Electronic Journal of Combinatorics},
  pages={R89-R89},
  year={2008},
  keywords={ACSV theory},
  url_Paper={https://www.combinatorics.org/ojs/index.php/eljc/article/view/v15i1r89/pdf},
  abstract={Let $\sum_{\beta\in\mathbb{N}^d} F_\beta x^\beta$ be a multivariate
power series, a generating function for a combinatorial class perhaps.
Assume that in a neighborhood of the origin this series represents a
nonentire function $F=G/H^p$ where $G$ and $H$ are holomorphic and $p$
is a positive integer. Given a direction $\alpha\in\mathbb{N}_+^d$ for
which asymptotics are controlled by a smooth point of the singular
variety $H = 0$, we compute the asymptotics of $F_{n\alpha}$ as
$n\to\infty$. 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 much
more accurate numerical approximation, as demonstrated in our examples.}
}

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