Name: On the asymptotics of a sequence of lacunary binomial-type polynomials
Creator: Richard B. Paris
Keywords: Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 0101 mathematics, 30E15, 41A60, 01 natural sciences

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2015Embargo end date: 01 Jan 2014 English Publisher:Element d.o.o.Journal:Journal of Classical Analysis (issn: 1848-5987,

Authors: Richard B. Paris;

doi: 10.7153/jca-06-04 , 10.48550/arxiv.1404.0217

arXiv: http://arxiv.org/abs/1404.0217

On the asymptotics of a sequence of lacunary binomial-type polynomials

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Abstract

We examine the asymptotics of a sequence of lacunary binomial-type polynomials $\wp_n(z)$ as $n\rightarrow\infty$ that have arisen in the problem of the expected number of independent sets of vertices of finite simple graphs. We extend the recent analysis of Gawronski and Neuschel by employing the method of steepest descents applied to an integral representation. The case of complex $z$ with $|z|<1$ is also considered. Numerical results are presented to illustrate the accuracy of the resulting expansions.

10 pages, 3 figures

Related Organizations

University of Abertay Dundee
United Kingdom

Keywords

Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 30E15, 41A60

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