What is the power series for $K_{\lambda}(w) = \int_{0}^{\infty}z^{\lambda-1}\exp\left\{-\frac{w}{2}\left(z + \frac{1}{z}\right)\right\}\mathrm{d}z$?

Question

As the title says, I would like to know what is the power series for (or at least a good approximation) \begin{align*} K_{\lambda}(w) = \frac{1}{2}\int_{0}^{\infty}z^{\lambda-1}\exp\left\{-\frac{w}{2}\left(z + \frac{1}{z}\right)\right\}\mathrm{d}z \end{align*}

Any reference would be appreciated.