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Hankel transform of (dirac delta)/k and of 1 
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#1
Feb612, 04:24 PM

P: 209

Hello Everyone,
I am wondering what the Hankel Transform of δ(k)/k is. ie: [itex]\int^{\infty}_{0}k\frac{\delta(k)}{k}J_{0}[k r] dk[/itex] = [itex]\int^{\infty}_{0}\delta(k) J_{0}[k r] dk[/itex] is. If the integral was from [itex]\infty to \infty[/itex], I know that it would be 1, and hence the hankel transform of 1 is δ(k)/k. But since the limits are from 0 to [itex]\infty[/itex], does the same result hold? The other two possibilities I see are 1/2 and 0. Thanks for your help. 


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