Dear colleagues, I want to know if there are some results on the bounds of modified Bessel functions $I_\alpha(x)$ and $K_\alpha(x)$? Especially, I need the exponential bounds for them, that is to say if it is possible to get a result like

$|I_\alpha(x)|\leq C exp(b x), x\geq 0$

where $C$ is a constant or a polynomial of $x$, b is a constant, $\alpha$ is a real number. Also the inequality of the same form about $K_\alpha(x)$.

Thank you in advance!