# Hankel transform of (dirac delta)/k and of 1

by osnarf
Tags: delta or k, dirac, hankel, transform
 P: 209 Hello Everyone, I am wondering what the Hankel Transform of δ(k)/k is. ie: $\int^{\infty}_{0}k\frac{\delta(k)}{k}J_{0}[k r] dk$ = $\int^{\infty}_{0}\delta(k) J_{0}[k r] dk$ is. If the integral was from -$\infty to \infty$, 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 $\infty$, does the same result hold? The other two possibilities I see are 1/2 and 0. Thanks for your help.