A new type of sharp bounds for ratios of modified Bessel functions
Classical Analysis and ODEs
2016-06-08 v1
Abstract
The bounds for the ratios of first and second kind modified Bessel functions of consecutive orders are important quantities appearing in a large number of scientific applications. We obtain new bounds which are accurate in a large region of parameters and which are shaper than previous bounds. The new bounds are obtained by a qualitative analysis of the Riccati equation satisfied by these ratios. A procedure is considered in which the bounds obtained from the analysis of the Riccati equation are used to define a new function satisfying a new Riccati equation which yields sharper bounds. Similar ideas can be applied to other functions.
Keywords
Cite
@article{arxiv.1606.02008,
title = {A new type of sharp bounds for ratios of modified Bessel functions},
author = {D. Ruiz-Antolin and J. Segura},
journal= {arXiv preprint arXiv:1606.02008},
year = {2016}
}
Comments
To appear in J. Math. Anal. Appl