AbstractIn this paper, we give the characteristic estimation of a meromorphic function f with the differential polynomials $f^{l}(f^{(k)})^{n}$
f
l
(
f
(
k
)
)
n
and obtain that $$\begin{aligned} T(r,f)\leq M\overline{N} \biggl(r,\frac{1}{f^{l}(f^{(k)})^{n}-a} \biggr)+S(r,f) \end{aligned}$$
T
(
r
,
f
)
≤
M
N
‾
(
r
,
1
f
l
(
f
(
k
)
)
n
−
a
)
+
S
(
r
,
f
)
holds for $M=\min \{\frac{1}{l-2},6\}$
M
=
min
{
1
l
−
2
,
6
}
, integers $l(\geq 2)$
l
(
≥
2
)
, $n(\geq 1)$
n
(
≥
1
)
, $k(\geq 1)$
k
(
≥
1
)
, and a non-zero constant a. This quantitative estimate is an interesting and complete extension of earlier results. The value distribution of a differential monomial of meromorphic functions is also investigated.
Characteristic estimation of differential polynomials
