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.
"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