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Continuum Mechanics and Thermodynamics

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08-07-2023 | Original Article

On Schwartz–Villat’s formula for analytic functions

Authors: Marin Marin, Andreas Öchsner, M. M. Bhatti, Sorin Vlase

Published in: Continuum Mechanics and Thermodynamics | Issue 6/2023

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Abstract

In this present study, we intend to obtain a new criterion for the analyticity of a complex function. More exactly, we will deduce some concrete restrictions that must be performed by a function that is complex, is defined on the disc centred at the origin that has radius 1 (hereinafter referred to as the unit disc), which, in addition, is continuous on this disc, including its border, to be analytic on the open unit disc. After that, as applications, we will deduce the Schwartz–Villat’s formula in this context, and we will obtain the known Joukowski’s function.

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Title: On Schwartz–Villat’s formula for analytic functions
Authors: Marin Marin
Andreas Öchsner
M. M. Bhatti
Sorin Vlase
Publication date: 08-07-2023
Publisher: Springer Berlin Heidelberg
Published in: Continuum Mechanics and Thermodynamics / Issue 6/2023
Print ISSN: 0935-1175
Electronic ISSN: 1432-0959
DOI: https://doi.org/10.1007/s00161-023-01242-8

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