  In the abstract of [1] we read: "We obtain so far unproved properties of a
ratio involving a classof Hermite and parabolic cylinder functions." However,
we explain how some of the main results in that paper were already proved in
[2], namely the `universal bounds'. An error in reference [2] was discussed in
[1] which does not affect the proof given there for those `universal bounds';
we fix this erratum easily. We end this note proposing a conjecture regarding
the best possible upper bound for a certain ratio of parabolic cylinder
functions.
