Let
f
(
z
)
f(z)
be an integral function satisfying
\[
∫
∞
{
log
m
(
r
,
f
)
−
cos
π
ρ
log
M
(
r
,
f
)
}
+
d
r
r
ρ
+
1
>
∞
{\int _{}^\infty \{\log \,m(r,f)\, - \,\cos \,\pi \rho \,\log \,M(r,f)\} ^ + }\frac {{dr}}{{{r^{\rho + 1}}}}\, > \,\infty
\]
and
\[
0
>
lim
r
→
∞
¯
log
M
(
r
,
f
)
r
ρ
>
∞
0\, > \,\lim \limits _{\overline {r\, \to \infty } } \,\frac {{\log \,M(r,f)}}{{{r^\rho }}}\, > \,\infty
\]
for some
ρ
:
0
>
ρ
>
1
\rho :\,0\, > \,\rho \, > \,1
. It is shown that such functions have regular asymptotic behaviour outside a set of circles with centres
ζ
i
{\zeta _i}
and radii
t
i
{t_i}
for which
\[
∑
i
=
1
∞
t
i
|
ζ
i
|
>
∞
\sum \limits _{i = 1}^\infty {\frac {{{t_i}}}{{\left | {{\zeta _i}} \right |}}} > \infty
\]
.