Characteristic function of a meromorphic function and its derivatives

Authors

  • J. Wu Xianning Vocational and Technical College, P.O. Box 437100, Xianning, P. R. China
  • Z. Wu School of Mathematics and Statistics, Hubei University of Science and Technology, P.O. Box 437100, Xianning, P. R. China
Abstract:

In this paper, some results of Singh, Gopalakrishna and Kulkarni (1970s) have been extended to higher order derivatives. It has been shown that, if $sumlimits_{a}Theta(a, f)=2$ holds for a meromorphic function $f(z)$ of finite order, then for any positive integer $k,$ $T(r, f)sim T(r, f^{(k)}), rrightarrowinfty$ if $Theta(infty, f)=1$ and $T(r, f)sim (k+1)T(r, f^{(k)}), rrightarrowinfty$ if $Theta(infty, f)=0.$

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Journal title

volume 39  issue 6

pages  1117- 1123

publication date 2013-12-15

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