On the value distribution of \(ff^{(k)}\)
type: Item
instance of: scholarly article
title: On the value distribution of \(ff^{(k)}\)
zbMATH Open document ID: 0867.30023
author: Chungchun Yang
author: Pei-Chu Hu
published in: Kodai Mathematical Journal
publication date: 1997-08-04T00:00:00Z
review text: If \(g\) is a transcendental entire function of finite order, then there exists at most one integer \(k\geq 2\), such that \(ff^{(k)}\) has a nonzero and finite Picard exceptional value. If \(f\) is a transcendental meromorphic function, we have that 1) for nonnegative integers \(n,n_1, \dots, n_k\) with \(n\geq 1\), \(d=n_1+ \cdots +n_k\geq 1\), if \(\delta\) \((0,f)> 3/(3d +1)\), then \(f^n(f')^{n_1} \dots (f^{(k)})^{n_k}\) has no finite nonzero Picard exceptional value. 2) under certain conditions, for \(c\in \mathbb{R}\setminus\{0\}\), \[ T(r,f)\leq \left(4+{1 \over k+1}\right) \left\{\overline N(r,f)+ \overline N \left(r, {1\over fP(f)-c} \right)\right\} +S(r,f), \] where \(P(f)\) is a class of differential polynomials.
reviewed by: Daochun Sun
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 949858
zbMATH Keywords: entire function
zbMATH Keywords: exceptional value
zbMATH Keywords: meromorphic function
zbMATH Keywords: differential polynomial
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138043595
OpenAlex ID: W2048897682
cites work: Q4218571
cites work: On the singularities of the inverse to a meromorphic function of finite order
cites work: On a Result of Hayman
cites work: Picard values of meromorphic functions and their derivatives
cites work: Q5540608
cites work: Q5723337
cites work: Über die Werteverteilung von \(f^{k+1}(k)\)
cites work: Q3361104
cites work: Über ein Problem von Hayman
cites work: Deficiencies of monomials
cites work: Über die Nullstellen von Differentialpolynomen
cites work: Über eine Borelsche Identität
cites work: Q3227756
cites work: Angular distribution of values of \(ff'\)
cites work: Q4288996
cites work: On monomials and Hayman's problem
DOI: 10.2996/KMJ/1138043595
description: scientific article; zbMATH DE number 949858