Equation containing modified bessel functions and exponential function

Question

I'm trying to find a approximation solution for the following equation: ${e^{ - x}}\left[ {{I_o}\left( x \right) + {I_1}\left( x \right)} \right] = C$ where $I_0$ and $I_1$ is the modified Bessel functions of the first kind of order 0 and 1. C is a constant. Do you have any suggestion? Thank you.

Answer 1

In the limit of large $x$, the left hand side looks like $\sqrt{2/(\pi x)}$, which results in equation that is easily soluble for $x$, so long as $C$ is sufficiently small.