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Integral of Bessel function, square root and gaussian

  1. Jul 8, 2011 #1
    Hi! Does anyone know how to solve the following integral analitically?

    [itex]\int^{1}_{0} dx \ e^{B x^{2}} J_{0}(i A \sqrt{1-x^{2}})[/itex], where A and B are real numbers.

  2. jcsd
  3. Jul 14, 2011 #2


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    Gold Member

    Not really sure, but maybe if I take a stab at the question, someone else will answer better.

    would it help to replace x=cos(θ)? then x^2 = cos^2(θ), dx =-sin(θ)dθ, [itex]\sqrt{1-x^2}=sin(\theta)[/itex] and have your integral go from θ= ∏/2 to 0.

    and you might try looking carefully at each of the "recurrence relations" for Bessel functions and see if they help.
    Last edited: Jul 14, 2011
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