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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: 2020-05
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 J. Math., Vol.24, No.6, pp.1353 - 1382
Data Type: article
DOI 連結:
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