hankel transform of (dirac delta)/k and of 1

osnarf

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.