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https://ah.lib.nccu.edu.tw/handle/140.119/135222
題名: | On binomial and Poisson sums arising from the displacement of randomly placed sensors | 作者: | 符麥克 Fuchs, Michael Kao, Louis Wu, Wan-Zhen |
貢獻者: | 應數系 | 關鍵詞: | asymptotics ; displacement cost ; generating functions ; Laplace method ; sensor | 日期: | Dec-2020 | 上傳時間: | 27-May-2021 | 摘要: | 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. | 關聯: | Taiwanese J. Math., Vol.24, No.6, pp.1353 - 1382 | 資料類型: | article | DOI: | https://doi.org/10.11650/tjm/200503 |
Appears in Collections: | 期刊論文 |
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