Is There a Closed Form for Airy Disk Eigenfunctions?

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marcusl
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Does anyone know if the eigenfunctions of the Airy disk function (or Bessel function) [tex]\frac{J_1(x)}{x}[/tex] has a closed form?
 
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From what I have seen on the internet, the answer is probably no. There are many publications and neither mentioned one, only approximations like the first zero and calculation of angles.
 

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