A further discussion of Radon’s problem for curves in the plane given, for fixed
(
p
,
ϕ
)
(p,\phi )
, by
r
α
cos
{
α
(
θ
−
ϕ
)
}
=
p
α
{r^\alpha }\cos \{ \alpha (\theta - \phi )\} = {p^\alpha }
.
α
\alpha
real,
α
≠
0
\alpha \ne 0
. Functions yielding null transforms, and zeros of the Fourier components of the transforms are given for general
α
\alpha
. and several orthogonal expansions are given for
α
=
±
1
/
m
\alpha = \pm 1/m
.
m
=
1
,
2
,
3
…
.
m = 1,2,3 \ldots .