Journal of East China Normal University(Natural Sc ›› 2014, Vol. 2014 ›› Issue (4): 8-17.

• Article • Previous Articles     Next Articles

On the kth derivatives of meromorphic functions and rational functions

YANG Pai1, LIU Xiao-jun2   

  1. 1. 成都信息工程学院~应用数学学院, 成都 610225;
    2. 上海理工大学~数学系, 上海 200093
  • Received:2013-07-01 Revised:2013-10-01 Online:2014-07-25 Published:2014-07-25

Abstract: Let $f$ be a transcendental meromorphic function in
$\mathbb C$, $R\not\equiv0$
 be a rational function,
 and let $k$ be a positive integer.
 Suppose that all zeros of $f$ have multiplicity at least $k+1$,
 except possibly finite many.
 Then $f^{(k)}-R$ has infinitely many zeros.

Key words: meromorphic function, Julia exceptional function, quasinormal family

CLC Number: