Titel
Elliptic Solutions of Dynamical Lucas Sequences
Autor*in
Meesue Yoo
Department of Mathematics, Chungbuk National University
Abstract
We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system is given by elliptic numbers. The second type involves a non-commutative version of Lucas sequences which defines the non-commutative (or abstract) Fibonacci polynomials introduced by Johann Cigler. If the non-commuting variables are specialized to be elliptic-commuting variables the abstract Fibonacci polynomials become non-commutative elliptic Fibonacci polynomials. Some properties we derive for these include their explicit expansion in terms of normalized monomials and a non-commutative elliptic Euler–Cassini identity.
Stichwort
Lucas sequencestheta functionselliptic numbersnon-commutative Fibonacci polynomials
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
https://phaidra.univie.ac.at/o:1597669
Erschienen in
Titel
Entropy
Band
23
Ausgabe
2
ISSN
1099-4300
Erscheinungsdatum
2021
Seitenanfang
183
Verlag
MDPI AG
Projektnummer
P32305 – Austrian Science Fund (FWF)
Erscheinungsdatum
2021
Zugänglichkeit
Rechteangabe
© 2021 by the authors

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