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About bessel function integrals

  1. Jul 2, 2011 #1
    hello,everyone
    i want to know how to solve this bessel function integrals:

    \int_{0}^{R} J_m-1(ax)*J_m+1 (ax)*x dx
    where J_m-1 and J_m+1 is the Bessel function of first kind, and a is a constant.

    thanks.
     
  2. jcsd
  3. Jul 2, 2011 #2
    Is this what you meant to post?

    [tex]\int_{0}^{R} J_{m-1}(ax)*J_{m+1} (ax)*x \ dx[/tex]

    I am not an expert on Bessel functions, but isn't there an identity that you can use to simplify this expression? Something like

    [tex]J_{m+1} = Some \ function \ of \ J_m[/tex]

    In other words, each successive Bessel function can be defined in terms of its predecessor. For example,

    J1 = some function of J0,
    J2 = some function of J1,
    J3 = some function of J2,
    J4 = some function of J3,
    etc.

    If you can find this identity, you should be able to simplify your integral.
     
  4. Jul 2, 2011 #3

    LCKurtz

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    Last edited by a moderator: Apr 26, 2017
  5. Jul 2, 2011 #4
    Last edited by a moderator: Apr 26, 2017
  6. Jul 2, 2011 #5
    yes,it is.thanks for your suggestions.i have solved it.:smile:
     
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