Computation and analysis of the asymptotic expansions of the compound means

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摘要

We derive algorithms for computing asymptotic expansion of the composite mean of two arbitrary means M and N. Then we analyse asymptotic behaviour of the compound mean M ⊗ N. Examples and application to some classical means are also presented.

论文关键词：Asymptotic expansion,Compound mean,Power mean,Arithmetic–geometric mean

论文评审过程：Received 1 October 2016, Revised 19 December 2016, Accepted 9 January 2017, Available online 19 January 2017, Version of Record 19 January 2017.

论文官网地址：https://doi.org/10.1016/j.amc.2017.01.025