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Fourier Bessel series

  1. Jan 6, 2009 #1
    1. The problem statement, all variables and given/known data
    By appropriate limiting procedures prove the following expansion
    [tex]\frac{1}{\left(\rho^2+z^2\right)^{1/2}}=\int^{\infty}_{0} e^{-k\left|z\right|}J_{0}(k\rho)dk[/tex]


    2. Relevant equations



    3. The attempt at a solution

    I tried to implicate the fourier-bessel series but it turned out that there is no k dependence on coefficients of the series.

    What can I do to proceed this question?
     
  2. jcsd
  3. Jan 7, 2009 #2
    I think you should write out the integral representation of this 0-order bessel function, and then switch the integrals. With this you get a 2D fourier transform of the given function.
    After all, the Hankel-transform with zero order bessel functions, is the 2D fourier transform of some cylindricaly symmetric two variable function.
     
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