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Bessel function

  1. Sep 15, 2008 #1
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Sep 17, 2008 #2


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    Since [tex]y' (x)[/tex] contains only odd powers of x, the n=1 term does not vanish when you take the derivative of the series. Therefore,

    [tex]y'' (x)= \sum_{n=1}^{\infty} \frac{(-1)^n (2n)(2n-1) x^{2n-2}}{4^n (n!)^2} [/tex]

    The extra [tex] x/2 [/tex] in your answer will be canceled by the [tex] n=1 [/tex] term.
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