Expansion of $\exp(\text{-constant}\times x)$ in terms of modified Bessel function

Question

Does anyone know a reference that has mentioned the following expansion of $e^{-\beta x}$ in terms of modified Bessel functions?

$$e^{-\beta x}=e^{-\beta b}\sum_s (-1)^s I_s(\beta r)e^{is \theta}$$

Does anyone know where can I find the proof for this?