Chapter 12.17, Problem 4P

Using (17.3) and the results stated in Problems 2 and 3 for $J_{1/2}$ and $Y_{1/2}\left(=N_{1/2}\right)$, show that $I_{1/2}(x)=\sqrt{\frac{2}{\pi x}}\sinh x,\text{ and }{K}_{1/2}(x)=\sqrt{\frac{\pi }{2x}}{e}^{-x}$.