Characteristic function of a meromorphic function and its derivatives

Wu, J.; Wu, Z.

Characteristic function of a meromorphic function and its derivatives

Document Type : Research Paper

Authors

J. Wu ¹

Z. Wu ²

¹ Xianning Vocational and Technical College, P.O. Box 437100, Xianning, P. R. China

² 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 $Theta(infty, f)=0.$

Keywords

characteristic function

Nevanlinna's deficiency

maximum deficiency sum

Subjects