Chapter 12.18, Problem 5P

Use the recursion relations of Section 15 (for $N^{\prime }$ s as well as for $J$ s) and Problem 4 to show that $J_n(x)N_{n+1}(x)-J_{n+1}(x)N_n(x)=-\frac{2}{\pi x}$.

Hint: Do it first for $n=0;$ then use the result in proving the $n=1$ case, and so on.