The Radon Transform on a Family of Curves in the Plane. II

A further discussion of Radon's problem for curves in the plane given, for fixed , by <!-- MATH ${r^\alpha }\cos \{ \alpha (\theta - \phi )\} = {p^\alpha }$ --> . real, <!-- MATH $\alpha \ne 0$ --> . Functions yielding null transforms, and zeros of the Fourier components of the transforms are given for general . and several orthogonal expansions are given for <!-- MATH $\alpha = \pm 1/m$ --> . <!-- MATH $m = 1,2,3 \ldots .$ -->