Redheffer type bounds for Bessel and modified Bessel functions of the first kind
Classical Analysis and ODEs
2017-01-31 v1
Abstract
In this paper our aim is to show some new inequalities of Redheffer type for Bessel and modified Bessel functions of the first kind. The key tools in our proofs are some classical results on the monotonicity of quotients of differentiable functions as well as on the monotonicity of quotients of two power series. We use also some known results on the quotients of Bessel and modified Bessel functions of the first kind, and by using the monotonicity of the Dirichlet eta function we prove a sharp inequality for the tangent function. At the end of the paper a conjecture is stated, which may be of interest for further research.
Keywords
Cite
@article{arxiv.1701.08446,
title = {Redheffer type bounds for Bessel and modified Bessel functions of the first kind},
author = {Árpád Baricz and Khaled Mehrez},
journal= {arXiv preprint arXiv:1701.08446},
year = {2017}
}