Hornik, Kurt, Grün, Bettina. 2013. Amos-type bounds for modified Bessel function ratios.. Journal of Mathematical Analysis and Applications 408 (1): 91-101.
BibTeX
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.
Tags
Press 'enter' for creating the tagPublication'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 |
Associations
- People
- Hornik, Kurt (Details)
- Grün, Bettina (Details)
- Organization
- Institute for Statistics and Mathematics IN (Details)
- Research Institute for Computational Methods FI (Details)