New Bounds for the Modified Bessel Function of the First Kind and Toader-Qi Mean

Abstract

Let Ipx be the modified Bessel function of the first kind of order p. The upper and lower bounds in the form of simple rational functions about cosht and (sinht)/t for the function I0x are obtained. The corresponding inequalities for the Toader-Qi mean do not match those in the existing literature.

Keywords

• bounds
• modified Bessel function of the first kind
• hyperbolic function
• mean
• inequality