New Properties and Matrix Representations on Higher-Order Generalized Fibonacci Quaternions with q-Integer Components

In this paper, by using q-integers and higher-order generalized Fibonacci numbers, we define the higher-order generalized Fibonacci quaternions with q-integer components. We give some special cases of these newly established quaternions. This article examines q-calculus and quaternions together. We...

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Bibliographic Details
Published inAxioms Vol. 13; no. 10; p. 677
Main Authors Kızılateş, Can, Du, Wei-Shih, Terzioğlu, Nazlıhan, Chen, Ren-Chuen
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.10.2024
Subjects
Binet formula
Calculus
Fibonacci numbers
Fibonacci quaternions
higher-order generalized Fibonacci numbers
Integers
Mathematicians
Matrices
Matrix representation
Number systems
q-calculus
q-integer
Quaternions
recurrence relation
Turkey
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Summary:In this paper, by using q-integers and higher-order generalized Fibonacci numbers, we define the higher-order generalized Fibonacci quaternions with q-integer components. We give some special cases of these newly established quaternions. This article examines q-calculus and quaternions together. We obtain a Binet-like formula, some new identities, a generating function, a recurrence relation, an exponential generating function, and sum properties of quaternions with quantum integer coefficients. In addition, we obtain some new identities for these types of quaternions by using three new special matrices.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13100677