1Department of Mathematics Nanjing Normal University Nanjing 210046, P.R. China 2Department of Applied Mathematics Nanjing Audit University Nanjing 210029, P.R. China
Annales Polonici Mathematici, Tome 98 (2010) no. 3, pp. 283-289
Let $f$ be a transcendental meromorphic function of infinite order
on $\mathbb{C}$, let $k\in \mathbb{N}$ and $\varphi=Re^P$, where
$R\not\equiv 0$ is a rational function and $P$ is a polynomial, and
let $a_0, a_1, \ldots, a_{k-1}$ be holomorphic functions on
$\mathbb{C}$. If all zeros of $f$ have multiplicity at least $k$ except
possibly finitely many, and $f=0\Leftrightarrow
f^{(k)}+a_{k-1}f^{(k-1)}+\cdots+a_0f=0$,
then $f^{(k)}+a_{k-1}f^{(k-1)}+\cdots+a_0f-\varphi$ has infinitely many zeros.
Keywords:
transcendental meromorphic function infinite order mathbb mathbb varphi where equiv rational function polynomial ldots k holomorphic functions mathbb zeros have multiplicity least except possibly finitely many leftrightarrow k k cdots k k cdots f varphi has infinitely many zeros
Affiliations des auteurs :
Yan Xu
1
;
Huiling Qiu
2
1
Department of Mathematics Nanjing Normal University Nanjing 210046, P.R. China
2
Department of Applied Mathematics Nanjing Audit University Nanjing 210029, P.R. China
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author = {Yan Xu and Huiling Qiu},
title = {On the value distribution of differential
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journal = {Annales Polonici Mathematici},
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Yan Xu; Huiling Qiu. On the value distribution of differential
polynomials of meromorphic functions. Annales Polonici Mathematici, Tome 98 (2010) no. 3, pp. 283-289. doi: 10.4064/ap98-3-7
