On the order and the lower order of differential polynomials

Authors

  • Kit-Wing Yu Department of Mathematics, United Christian College, 7-11, Tong Yam Street, Tai Hang Tung, Kowloon, Hong Kong, China.
  • Milind-Narayanrao Kulkarni Department ofMathematics, Karnatak University, Dharwad, India.

DOI:

https://doi.org/10.5556/j.tkjm.42.2011.647

Keywords:

Differential polynomials, homogeneous, lower order, meromorphic functions, Nevanlinna theory, non-homogeneous, order

Abstract

Suppose that $f$ is a meromorphc function with order $\sigma(f)$ and lower order $\mu(f)$. Suppose that $P[f]$ is a differential polynomial of $f$. In this paper, it is shown that the order and the lower order of $P[f]$ are equal to the order and the lower order of $f$ under certain conditions on the degree of the differential polynomial $P[f]$, \textit{i.e.}, $\sigma(P)=\sigma(f)$ and $\mu(P)=\mu(f)$. This result improves previous results.

References

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Published

2011-12-31

How to Cite

Yu, K.-W., & Kulkarni, M.-N. (2011). On the order and the lower order of differential polynomials. Tamkang Journal of Mathematics, 42(4), 475–482. https://doi.org/10.5556/j.tkjm.42.2011.647

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Section

Papers