It is shown that for any limit-circle expression
L
(
y
)
=
Σ
j
=
0
n
p
j
y
(
j
)
L(y) = \Sigma _{j = 0}^n {{p_j}{y^{(j)}}}
, any sequence of disjoint intervals
{
[
a
k
,
b
k
]
}
k
=
1
∞
\{ [{a_k},{b_k}]\} _{k = 1}^\infty
such that
a
k
→
∞
{a_k} \to \infty
as
k
→
∞
k \to \infty
, and any
i
⩽
n
−
1
i \leqslant n - 1
, there is an expression
M
(
y
)
=
Σ
j
=
0
n
q
j
y
(
j
)
M(y) = \Sigma _{j = 0}^n {{q_j}{y^{(j)}}}
such that
q
i
=
p
i
{q_i} = {p_i}
except on
∪
(
a
k
,
b
k
)
,
q
j
=
p
j
\cup ({a_k},{b_k}),{q_j} = {p_j}
for all
j
≠
i
j \ne i
, and such that
M
M
is not limit-circle.