(ii) Let Jp(x) denote a Bessel function of the first kind of order p. Prove the following identities: d dx (x pJp(x)) = x pJp−1(x), and d dx ( x −pJp(x) ) = −x −pJp+1(x) The using the above identities to prove that Jp+1(x) = 2p x Jp(x) − Jp−1(x)
Use (ii) to to rewrite the Bessel function of zero order and first kind J0(x) in terms of J−1(x) and J−2(x)
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