Question: 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
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 \((6.60)\).
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