Results 1 to 10 of about 1,567,212 (302)
Fractal and Fractional, 2023 The composition H(z)=f(Φ(z)) is studied, where f is an entire function of a single complex variable and Φ is an entire function of n complex variables with a vanished gradient.
Andriy Bandura +2 more
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Logarithmic derivative of an entire function [PDF]
Proceedings of the American Mathematical Society, 1971 A representation for the logarithmic derivative ( f ′ / f ) (f’/f) of an entire function f f of finite order, parametrically in terms of some zeros and critical points of f f , is derived from the Hadamard representation and ...
Morris Marden
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An Entire Holomorphic Function Associated to an Entire Harmonic Function
Journal of Approximation Theory, 1999 Given a harmonic function \(h\) on \(\mathbb{R}^N\), \(N\geq 2\), \((h\in {\mathcal H}_N)\) there is a unique holomorphic function \(f\) on \(\mathbb{C}\), \((f\in{\mathcal E})\) such that \(f(t)=h(t,0,\dots,0)\) for \(t\in\mathbb{R}\). This paper has two purposes. Firstly to obtain theorems on the connection between the growth rates of \(h\) and \(f\)
Armitage, D.H.
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Asymptotic Functions of Entire Functions [PDF]
Computational Methods and Function Theory, 2021 If $f$ is an entire function and $a$ is a complex number, $a$ is said to be an asymptotic value of $f$ if there exists a path $γ$ from $0$ to infinity such that $f(z) - a$ tends to $0$ as $z$ tends to infinity along $γ$. The Denjoy--Carleman--Ahlfors Theorem asserts that if $f$ has $n$ distinct asymptotic values, then the rate of growth of $f$ is at ...
Hinkkanen, Aimo +2 more
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On the growth of entire solution of a nonlinear differential equation [PDF]
Mathematica Bohemica, 2020 In the paper we consider the growth of entire solution of a nonlinear differential equation and improve some existing results.
Indrajit Lahiri, Shubhashish Das
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Further study on the Brück conjecture and some non-linear complex differential equations [PDF]
Arab Journal of Mathematical Sciences, 2021 Purpose – The purpose of this current paper is to deal with the study of non-constant entire solutions of some non-linear complex differential equations in connection to Brück conjecture, by using the theory of complex differential equation.
Dilip Chandra Pramanik, Kapil Roy
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On the distribution of unique range sets and its elements over the extended complex plane
Математичні Студії, 2023 In the paper, we discussed the distribution of unique range sets and its elements over the extended complex plane from a different point of view and obtained some new results regarding the structure and position of unique range sets.
S. Mallick
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No Entire Inner Functions [PDF]
Analysis Mathematica, 2020 6 pages, doubling condition ...
Cobos, A., Seco Forsnacke, Daniel
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Normality and uniqueness of homogeneous differential polynomials
Математичні Студії, 2023 The primary goal of this work is to determine whether the results from [19, 20] still hold true when a differential polynomial is considered in place of a differential monomial.
R. S. Dyavanal, S. B. Kalakoti
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Minimal growth of entire functions with prescribed zeros outside exceptional sets
Математичні Студії, 2022 Let $h$ be a positive continuous increasing to $+\infty$ function on $\mathbb{R}$.
I. Andrusyak, P. Filevych, O. Oryshchyn
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