Rad HAZU, Matematičke znanosti, Vol. 29 (2025), 231-241.

ASYMPTOTIC BEHAVIOUR OF THE QUASI-ARITHMETIC MEANS

Neven Elezović and Lenka Mihoković

Abstract.   In this paper we study the asymptotic behaviour of the quasi-arithmetic means M_φ, 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.

2020 Mathematics Subject Classification.   41A60, 26E60.

Key words and phrases.   Asymptotic expansion, quasi-arithmetic mean, digamma function.

DOI: https://doi.org/10.21857/ydkx2cvdg9

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