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政大典藏 > College of Science > Department of Mathematical Sciences > Periodical Articles > Item 140.119/135222

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/135222

Title:	On binomial and Poisson sums arising from the displacement of randomly placed sensors
Authors:	符麥克 Fuchs, Michael Kao, Louis Wu, Wan-Zhen
Contributors:	應數系
Keywords:	asymptotics;displacement cost;generating functions;Laplace method;sensor
Date:	2020-12
Issue Date:	2021-05-27 11:41:50 (UTC+8)
Abstract:	We re-visit the asymptotics of a binomial and a Poisson sum which arose as (average) displacement costs when moving randomly placed sensors to anchor positions. The first-order asymptotics of these sums were derived in several stages in a series of recent papers. In this paper, we give a unified approach based on the classical Laplace method with which one can also derive more terms in the asymptotic expansions. Moreover, in a special case, full asymptotic expansions can be given which even hold as identities. This will be proved by a combinatorial approach and systematic ways of computing all coefficients of these identities will be discussed as well.
Relation:	Taiwanese Journal of Mathematics, Vol.24, No.6, pp.1353-1382
Data Type:	article
DOI link:	https://doi.org/10.11650/tjm/200503
DOI:	10.11650/tjm/200503
Appears in Collections:	[Department of Mathematical Sciences] Periodical Articles

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