Amos-type bounds for modified Bessel function ratios.

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Abstract

We systematically investigate lower and upper bounds for the modified Bessel function ratio Rν=Iν+1/Iν by functions of the form View the MathML source in case Rν is positive for all t>0, or equivalently, where ν≥−1 or ν is a negative integer. For ν≥−1, we give an explicit description of the set of lower bounds and show that it has a greatest element. We also characterize the set of upper bounds and its minimal elements. If ν≥−1/2, the minimal elements are tangent to Rν in exactly one point 0≤t≤∞, and have Rν as their lower envelope. We also provide a new family of explicitly computable upper bounds. Finally, if ν is a negative integer, we explicitly describe the sets of lower and upper bounds, and give their greatest and least elements, respectively.
Original languageEnglish
Pages (from-to)91 - 101
JournalJournal of Mathematical Analysis and Applications
Volume408
Issue number1
DOIs
Publication statusPublished - 1 Oct 2013

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