Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39620131215Characteristic function of a meromorphic function and its derivatives11171123464ENJ.WuXianning Vocational and Technical College,
P.O. Box 437100, Xianning, P. R. ChinaZ.WuSchool of Mathematics and Statistics, Hubei University of Science and Technology,
P.O. Box 437100, Xianning, P. R. ChinaJournal Article20110720In this paper, some results of Singh, Gopalakrishna and <br />Kulkarni (1970s) have been extended to higher order derivatives. It <br />has been shown that, if $sumlimits_{a}Theta(a, f)=2$ holds for a <br />meromorphic function $f(z)$ of finite order, then for any positive <br />integer $k,$ $T(r, f)sim T(r, f^{(k)}), rrightarrowinfty$ if <br />$Theta(infty, f)=1$ and $T(r, f)sim (k+1)T(r, f^{(k)}), <br />rrightarrowinfty$ if $Theta(infty, f)=0.$http://bims.iranjournals.ir/article_464_28b526931ff60ee50847aaedcce35cc0.pdf