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

Let I-p(x) 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.

Automated summary

The upper and lower bounds in the form of simple rational functions about cosht and (sinht)/t for the function I0x are obtained, and the corresponding inequalities for the Toader-Qi mean do not match those in the existing literature.