A complete asymptotic expansion of power means
type: Item
instance of: scholarly article
title: A complete asymptotic expansion of power means
zbMATH Open document ID: 1104.41015
author: Ulrich Abel
author: Mircea Ivan
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-12-07T00:00:00Z
review text: Let \(x_j>0\), \(w_j\geq 0\) \((j=1,\dots,n)\), \(\sum_{j=1}^n w_j=1\) and \(M_p(\mathbf{x}):= (\sum_{j=1}^n w_j x_j^p)^{1/p}\) for \(p\neq 0\) and \(M_0(\mathbf{x}):= \prod_{j=1}^n x_j^{w_j}.\) The authors' purpose is to give a complete asymptotic expansion of \(M_p({\mathbf x}+{\mathbf a})\) in terms of partial exponential Bell polynomials.
reviewed by: János Aczél
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 33E50
zbMATH DE Number: 5078946
zbMATH Keywords: Asymptotic expansions
zbMATH Keywords: Bell polynomials
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.01.089
OpenAlex ID: W2028617750
Wikidata QID: Q115600873
cites work: Q4769056
cites work: Inequalities for generalized weighted mean values of convex function
cites work: Q4405392
DOI: 10.1016/J.JMAA.2006.01.089
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description: scientific article; zbMATH DE number 5078946