prove that :

$\displaystyle { \displaystyle J\scriptscriptstyle -p(x) } = ( -1)^{p} \displaystyle J\scriptscriptstyle p (x) $

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- May 22nd 2009, 12:02 PMflower3Bessel's equation
prove that :

$\displaystyle { \displaystyle J\scriptscriptstyle -p(x) } = ( -1)^{p} \displaystyle J\scriptscriptstyle p (x) $ - May 23rd 2009, 08:52 AMthe_doc
First I'm assuming you meant to write:

$\displaystyle J_{-p}(x) = (-1)^{p} J_{p} (x)$ .

Chapter 11 of Mathematical methods for physicists by Arfken shows how it is done from the generating function.