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!



About the exponential bounds for modified Bessel function
There are some bounds of that form in [this paper](http://www.bepress.com/cgi/viewcontent.cgi?article=1064&context=mdandersonbiostat). See also the first reference at the end of the paper.


