English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $F(x)= \sum_{\nu\in\NN^d} F_\nu x^\nu$ be a multivariate power serieswith complex coefficients that converges in a neighborhood of the origin.Assume $F=G/H$ for some functions $G$ and $H$ holomorphic in a neighborhood ofthe origin. We derive asymptotics for the coefficients $F_{r\alpha}$ as $r \to\infty$ with $r\alpha \in \NN^d$ for $\alpha$ in a permissible subset of$d$-tuples of positive reals. More specifically, we give an algorithm forcomputing arbitrary terms of the asymptotic expansion for $F_{r\alpha}$ whenthe asymptotics are controlled by a transverse multiple point of the analyticvariety $H = 0$. This improves upon earlier work by R. Pemantle and M. C.Wilson.  We have implemented our algorithm in Sage and apply it to obtain accuratenumerical results for several rational combinatorial generating functions.

Asymptotics of coefficients of multivariate generating functions: improvements for multiple points