Fourier Transform of Bessel Function of the 1st Kind

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SUMMARY

The discussion centers on the Fourier Transform of the Bessel Function of the 1st Kind, specifically addressing the challenges faced in part (b) of a related problem. The participant successfully solved part (a) but expressed uncertainty regarding the application of delta function properties in part (b). The solution is available on Math Stack Exchange, providing a comprehensive approach to the problem.

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Airsteve0
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I would be grateful if someone could help me out with the problem that I have attached. I believe I have successfully answered part (a) of the question but am completely unsure of how to approach part (b). I realize it must have to do with specific properties of the delta function but I am lost. Any assistance would be greatly appreciated, thanks.
 

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thank you very much
 

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