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

RIS

@ARTICLE{Hornik2013,
title = {Amos-type bounds for modified Bessel function ratios.},
author = {Kurt Hornik and Bettina Grün},
year = {2013},
url = {http://www.sciencedirect.com/science/article/pii/S0022247X13005374?np=y},
volume = {408},
number = {1},
language = {EN},
pages = {91-101},
journal = {Journal of Mathematical Analysis and Applications},
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.},
}