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Bessel function

  1. Sep 15, 2008 #1
    1. The problem statement, all variables and given/known data
    http://g.imageshack.us/img114/questionta3.jpg/1/ [Broken]

    2. Relevant equations

    3. The attempt at a solution

    May I know which part of my solution went wrong? In the end the answer gives x/2 instead of 0.
    Last edited by a moderator: Apr 23, 2017 at 3:43 PM
  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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