Some results are obtained concerning the signs of the coefficients in the expansions in powers of
x
−
1
,
(
1
+
x
)
−
1
{x^{ - 1}},{(1 + x)^{ - 1}}
or
(
1
−
x
)
−
1
{(1 - x)^{ - 1}}
of
1
/
p
n
(
x
)
1/{p_n}(x)
and
q
n
(
x
)
{q_n}(x)
, where
p
n
(
x
)
{p_n}(x)
is the polynomial of degree n in the orthogonal sequence associated with a given weight-function
w
(
x
)
w(x)
over
(
−
1
,
1
)
( - 1,1)
and
q
n
(
x
)
=
∫
−
1
1
w
(
t
)
p
n
(
t
)
(
x
−
t
)
−
1
d
t
{q_n}(x) = \smallint _{ - 1}^1w(t){p_n}(t){(x - t)^{ - 1}}dt
.