Some inequalities for modified bessel functions

Abstract

We denote by Iv and Kv the Bessel functions of the first and third kinds, respectively. Motivated by the relevance of the function wv (t)=t (Iv-1 (t) / Iv (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 Iv (t) / Iv-1 (t). The results are based on the recurrence relations for Iv and Iv-1 and the Turán-type inequalities for such functions. Similar investigations are developed to establish new inequalities for Kv (t) / K v-1 (t). Copyright © 2010 A. Laforgia and P. Natalini.