I wonder whether one could reduce the following integral to some combination of special (e.g. Bessel) functions: $$\int_{m}^{\infty}d\epsilon \exp\left(-s\epsilon\right)\left( \epsilon^{2}-m^{2}\right)^{1/2}\left( \epsilon^{2}-\lambda m^{2}\right)^{1/2}$$

The integral without the last term in the integrand reduces to a well know integral representation of $K_{1}$, but I can not figure out if there is a clever variable substitution which brings the integral above to something better known.