Original scientific paper
https://doi.org/10.21857/ydkx2cvdg9
Asymptotic behaviour of the quasi-arithmetic means
Neven Elezović
; Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000 Zagreb, Croatia
Lenka Mihoković
; Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000 Zagreb, Croatia
Abstract
In this paper we study the asymptotic behaviour of the quasi-arithmetic means Mφ, for large values of its arguments. We extend and simplify known results form the literature. Asymptotic expansions of these means are derived under very weak assumptions on a given function φ. The coefficients in the asymptotic expansions are defined by recursive formulas, and the general algorithms for their calculation are then demonstrated on some interesting examples of means.
Keywords
Asymptotic expansion; quasi-arithmetic mean; digamma function
Hrčak ID:
326524
URI
Publication date:
9.1.2025.
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