Real inversion formula for the generalized Hankel-Clifford transformation (Q1286985)

The author derives a real inversion formula for what he says is a generalized Hankel-Clifford transformation, viz., \[ J(y)= y^{\lambda/2} \int_0^\infty \tau^{-\lambda/2} J_\lambda (2\sqrt{y\tau})j(\tau)d\tau. \] It is obviously the classical Hankel transformation for the function \(\tau^{\frac 12(\lambda+1)} j(\tau)\) with kernel \(\sqrt{y\tau} J_\lambda (2\sqrt{y\tau})\). The author extends his results to generalized functions defined over certain spaces defined by him.