Chapter 12.15, Problem 6P

As in Problem 5, show that $J_{p-1}(x)=J_{p+1}(x)$ at every maximum or minimum of $J_p(x),$ and $J_{p-1}(x)=-J_{p+1}(x)=J_p^{\prime }(x)$ at every positive zero of $J_p(x).$ Computer plot, say, $J_2,J_3,$ and $J_4$ on the same axes, (or any other set of three consecutive $J$ ’s or three consecutive $N^{\prime }$s ) and check to see that the results are true.