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Keywords = Montel’s normalization

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15 pages, 277 KiB  
Article
Harmonic Functions with Montel’s Normalization
by Jacek Dziok
Symmetry 2025, 17(5), 720; https://doi.org/10.3390/sym17050720 - 8 May 2025
Viewed by 206
Abstract
In the Geometric Theory of Analytic Functions, classes of functions with several normalizations are considered. We consider the symmetric idea for harmonic functions. Classes of harmonic functions f with normalization f0=fz¯0=0, [...] Read more.
In the Geometric Theory of Analytic Functions, classes of functions with several normalizations are considered. We consider the symmetric idea for harmonic functions. Classes of harmonic functions f with normalization f0=fz¯0=0,fz0=1 are usually considered in the geometric theory of harmonic functions. The normalization is called the classical normalization. We can obtain some interesting results by using Montel’s normalization f0=fz¯0=0,fzρfz¯ρ=1, where ρ[0,1). In the paper, we consider the class of harmonic functions with Montel’s normalization associated with the generalized hypergeometric function. Full article
(This article belongs to the Special Issue Mathematics: Feature Papers 2025)
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