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Solve equations (15.1) and (15.2) for Jp+1(x) and Jp-1(x). Add and subtract these two equations to get (15.3) and (15.4). (15.1) la J,(r)] =

Solve equations (15.1) and (15.2) for Jp+1(x) and Jp-1(x). Add and subtract these two equations to get (15.3) and (15.4). (15.1) la" J,(r)] = r" Jp-1(x), dr d. [rPJp(x)] = --PJp+1(x), (15.2) dr Jp-1(x) + Jp+1(x) = "J,(x), Jp-1(x) Jp+1(a) = 2., (a), J,(x) = -J,(x) + Jp-1(r) = Jp(x) Jp+1(x). (15.3) (15.4) (15.5)

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