Total defect of a meromorphic function and all its derivatives
type: Item
instance of: scholarly article
title: Total defect of a meromorphic function and all its derivatives
zbMATH Open document ID: 0760.30012
DOI: 10.1007/BF03323110
author: Wang Yaofei
published in: Results in Mathematics
publication date: 1993-01-12T00:00:00Z
review text: Let \(f\) be a meromorphic function. In addition to the usual terminology of Nevanlinna theory, put \[ \theta_ j=j \liminf_{r\to\infty}{{\bar N(r,f)} \over {T(r,f^{(j)})}}. \] Then \(0\leq\theta_ j\leq{j \over {j+1}}<1\). It is proved that \[ \delta(0,f)+\sum_{j=0}^ n \left( {1\over {1-\theta_ j}} \sum_{a\in C\setminus\{0\}} \delta(a,f^{(j)})\right) +{1 \over {1-\theta_ n}} \delta(\infty,f^{(n)})\leq 2 \] for \(n\geq 0\) and \[ \sum_{a\in C} \delta(a,f)+\sum_{j=1}^ \infty \left( {1 \over {1-\theta_ j}} \sum_{b\in C\setminus\{0\}} \delta(b,f^{(j)})\right) \leq 2. \] One of the main tools used in the proof is a result of \textit{G. Frank} and \textit{G. Weissenborn} [Bull. Lond. Math. Soc. 18, 29-33 (1988; Zbl 0586.30025)].
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 30D30
zbMATH DE Number: 86374
zbMATH Keywords: meromorphic function
zbMATH Keywords: derivative
zbMATH Keywords: deficiency
reviewed by: Walter Bergweiler
MaRDI profile type: Publication
cites work: Q5810707
cites work: Q5523155
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cites work: On the zeros of linear differential polynomials of meromorphic functions
cites work: Eine Verallgemeinerung des zweiten Nevanlinnaschen Hauptsatzes.
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cites work: Precise fundamental inequalities and sum of deficiencies
full work available at URL: https://doi.org/10.1007/bf03323110
OpenAlex ID: W4236508954
description: scientific article; zbMATH DE number 86374