Open AccessOn the order and the lower order of differential polynomials
Author(s) -
Kit-Wing Yu,
Milind-Narayanrao Kulkarni
Publication year - 2011
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.42.2011.647
Subject(s) - order (exchange) , mathematics , sigma , polynomial , differential (mechanical device) , combinatorics , degree (music) , function (biology) , mathematical analysis , physics , quantum mechanics , finance , evolutionary biology , biology , acoustics , economics , thermodynamics
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 $P[f]$, extit{i.e.}, $sigma(P)=sigma(f)$ and $mu(P)=mu(f)$. This result improves previous results