Prove the following identities based on those in the Problem 14:

a. \(J_{p-1}(x)+J_{p+1}(x)=\frac{2 p}{x} J_{p}(x)\).

b. \(J_{p-1}(x)-J_{p+1}(x)=2 J_{p}^{\prime}(x)\).

Data from Problem 14

Use the infinite series in the Problem 13 derive the derivative identities \((6.59)\) and \((6.60)\).