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.
Citation
Michael Fuchs. Louis Kao. Wan-Zhen Wu. "On Binomial and Poisson Sums Arising from the Displacement of Randomly Placed Sensors." Taiwanese J. Math. 24 (6) 1353 - 1382, December, 2020. https://doi.org/10.11650/tjm/200503
Information