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Entire and Meromorphic Solutions of the Functional Equation $$f^n+g^n+h^n=1$$ f n + g n + h n = 1 and Differential Equations

Entire and Meromorphic Solutions of the Functional Equation $$f^n+g^n+h^n=1$$ f n + g n... In this paper, we study Fermat-type functional equations $$f^n+g^n+h^n=1$$ f n + g n + h n = 1 in the complex plane. Alternative proofs of the known results for entire and meromorphic solutions of such equations are given. Moreover, some conditions on degrees of polynomial solutions are given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Entire and Meromorphic Solutions of the Functional Equation $$f^n+g^n+h^n=1$$ f n + g n + h n = 1 and Differential Equations

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Publisher
Springer Journals
Copyright
Copyright © 2019 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-018-0258-y
Publisher site
See Article on Publisher Site

Abstract

In this paper, we study Fermat-type functional equations $$f^n+g^n+h^n=1$$ f n + g n + h n = 1 in the complex plane. Alternative proofs of the known results for entire and meromorphic solutions of such equations are given. Moreover, some conditions on degrees of polynomial solutions are given.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Jan 3, 2019

References