Chapter 6, Problem 23RE

(a)

To determine

To show: The expression $Y_{3/2}\left(x\right)=-\sqrt{\frac{2}{\pi x}}\left(\frac{\cos x}{x}+\sin x\right)$ using Bessel functions.

(b)

To determine

To show: The expression $I_{1/2}\left(x\right)=\sqrt{\frac{2}{\pi x}}\sinh x$ and $I_{-1/2}\left(x\right)=\sqrt{\frac{2}{\pi x}}\cosh x$ using equation $I_v\left(x\right)=i^{-v}{J}_v\left(ix\right)$.

(c)

To determine

To show: The expression $K_{1/2}\left(x\right)=\sqrt{\frac{\pi }{2x}}{e}^{-x}$ using recurrence relation.