Remarks on the paper: "Bounds for functions involving ratios of modified Bessel functions"

Details Remarks on the paper: "Bounds for functions involving ratios of modified Bessel functions" Remarks on the paper: "Bounds for functions involving ratios of modified Bessel functions"

2011-11-04

arxiv.org/abs/1111.1018v2

Mathematics

Classical Analysis and ODEs

A corrigendum by C. G. Kokologiannaki has already been published. See http://dx.doi.org/10.1016/j.jmaa.2011.11.020

Scientific paper

A recent paper by C.G. Kokologiannaki published in J. Math. Anal. Appl. \cite{Kolo:2012:BFI} gives some properties for ratios of modified Bessel functions and, in particular, some bounds. These bounds are said to improve the range of some inequalities in \cite{Segura:2011:BRM} or to be sharper. Unfortunately, Kokologiannaki made some mistakes in the comparison and no improvement or extension is made over the results in \cite{Segura:2011:BRM}. We explain the errors in these comments and show that the bounds given in \cite{Kolo:2012:BFI} are already contained in \cite{Segura:2011:BRM}.

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