In 1939, G. H. Hardy proved that, under certain conditions, the only functions satisfying
∫
0
1
f
(
λ
m
t
)
f
(
λ
n
t
)
d
t
=
0
,
\begin{equation*} \int _{0}^{1}f(\lambda _{m}t)f(\lambda _{n}t)dt=0, \end{equation*}
where the
λ
n
\lambda _{n}
are the zeros of
f
f
, are the Bessel functions. We replace the above integral by the Jackson
q
q
-integral and give the
q
q
-analogue of Hardy’s result.