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Is there somebody who knows the solution for the integral $$\int_0^\infty\frac{J^3_1(ax)J_0(bx)}{x^2} dx$$ where $a>0,b>0$ and $J(\cdot)$ the bessel function of the first kind with integer order?

Reference, or solution from computer programs all are welcome. Thanks!

  • 0
    Are you interested in a closed form (doesn't seem likely to me), or in a numerical method for computing this?2011-09-22
  • 0
    In any event, you might be interested in [this](http://dx.doi.org/10.1145/1186785.1186790) and [this](http://netlib.org/toms/858).2011-09-22
  • 1
    Thank you! It's interesting! But I need closed form. I already know it's 0 when $b>3a$. I want other cases. I wonder if Maple or Mathematica works for it. I have not these softwares on hand.2011-09-22

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