On the order and the lower order of differential polynomials | Zendy

Kit-Wing Yu | Zendy; Milind-Narayanrao Kulkarni | Zendy

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On 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

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