prove that : $\displaystyle \frac{d}{dx}[x^{-p} J \scriptscriptstyle p+1 \displaystyle (x) ] = \frac{2p}{x} J \scriptscriptstyle p \displaystyle (x) $
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Again I refer you to Chapter 11 of Mathematical methods for physicists by Arfken to do so directly from the generating function.
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