Inequalities for modified Bessel functions and their integrals

Abstract

Simple inequalities for some integrals involving the modified Bessel functions $I_{\nu}(x)$ and $K_{\nu}(x)$ are established. We also obtain a monotonicity result for $K_{\nu}(x)$ and a new lower bound, that involves gamma functions, for $K_0(x)$.Comment: 13 pages. Final version. To appear in Journal of Mathematical Analysis and Application