It is shown that
λ
x
n
,
k
(
λ
)
\lambda x_{n,k}^{(\lambda )}
increases as
λ
\lambda
increases for
0
>
λ
>
1
,
k
=
1
,
2
,
…
,
[
n
2
]
0 > \lambda > 1,k = 1,2, \ldots ,\left [ {\tfrac {n}{2}} \right ]
, where
x
n
,
k
(
λ
)
x_{n,k}^{(\lambda )}
is the
k
th
k{\text {th}}
positive zero of ultraspherical polynomial
P
n
(
λ
)
(
x
)
P_n^{(\lambda )}(x)
.
