Quotation Hornik, Kurt, Grün, Bettina. 2013. Amos-type bounds for modified Bessel function ratios.. Journal of Mathematical Analysis and Applications 408 (1): 91-101.


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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.

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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Journal article
Journal Journal of Mathematical Analysis and Applications
Citation Index SCI
Language English
Title Amos-type bounds for modified Bessel function ratios.
Volume 408
Number 1
Year 2013
Page from 91
Page to 101
URL http://www.sciencedirect.com/science/article/pii/S0022247X13005374?np=y

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People
Hornik, Kurt (Details)
Grün, Bettina (Details)
Organization
Institute for Statistics and Mathematics IN (Details)
Research Institute for Computational Methods FI (Details)
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