Year: 2026
Type: article
Abstract: Consider two positive nonzero numbers x1 and x2. In many cases the arithmetic (AM), geometric (GM) or harmonic mean (HM) is used as an appropriate mean x12 of x1 and x2: AM=(x1+x2)/2, GM=(x1 x2)^(1/2), and HM=GM^2/AM. However, sometimes it is not clear from the outset which mean value should be selected. This results in a discrete problem. Instead of this here we discuss three one-parameter functions, which are able to describe a continuous connection between the mean values HM, GM, and AM, respectively. Two of these functions are known as Lehmer mean and Hölder mean, whereby especially the latter function is suitable for generating a uniform one-parameter description of various mixing rules as used in quantum chemical force field calculations and thermophysical properties calculations.
Source: ACS Omega
Author: Uwe Hohm
Institution: Technische Universität Braunschweig
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,935
OpenAlex ID: W7127922134