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A difficult integral! for help!

  1. Sep 3, 2009 #1
    [tex]\int^{2a}_{0}dpJ[0,b\sqrt{p}]J[0,b\sqrt{2a-p}][/tex]

    where a and b are constant, and J[0,x] is Bessel function.
     
  2. jcsd
  3. Sep 5, 2009 #2

    benorin

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    Homework Helper

    Expand out both Bessel functions as a series and multiply them according to Cauchy's rule, namely

    [tex] \left(\sum_{k=0}^{\infty}a_{k} x^{k}\right) \left(\sum_{j=0}^{\infty}b_{j} x^{j}\right) = \sum_{k=0}^{\infty}\sum_{j=0}^{k}a_{j}b_{k-j} x^k[/tex]​

    and pass the integral through to the inner most sum (the second time I've blatantly ignored convergence issues, perfering to hand-wave such until I get a result) and make the change of variables [itex]p=2au[/itex], you should get it from there... post your result so I can compare/check my work.

    Ben
     
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