Copyright © 2010 Andrea Laforgia and Pierpaolo Natalini. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We denote by Iν and Kν the Bessel functions of the first and third kinds, respectively. Motivated by the relevance of the function wν(t)=t(Iν−1(t)/Iν(t)), t>0, in many contexts of applied mathematics and, in particular, in some elasticity problems Simpson and Spector (1984), we establish new inequalities for Iν(t)/Iν−1(t). The results are based on the recurrence relations for Iν and Iν−1 and the Turán-type inequalities for such functions. Similar investigations are developed to establish new inequalities for Kν(t)/Kν−1(t).