On hyper complex numbers with higher order Pell numbers components

In this article, we define higher order Pell numbers. Then we introduce a new family of hyper complex numbers by using higher order Pell numbers. We call these families as the higher order Pell 2 s -ions. We present some algebraic properties of the higher order Pell 2 s -ions such as recurrence rela...

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Bibliographic Details
Published inThe Journal of Analysis Vol. 31; no. 4; pp. 2443 - 2457
Main Author Özimamoğlu, Hayrullah
Format Journal Article
LanguageEnglish
Published Singapore Springer Nature Singapore 01.12.2023
Subjects
Abstract Harmonic Analysis
Analysis
Fourier Analysis
Functional Analysis
Mathematics
Mathematics and Statistics
Measure and Integration
Original Research Paper
Special Functions
Hyper complex numbers
11B83
Recurrence relation
11R52
Higher order Pell hyper complex numbers
Binet’s formula
Higher order Pell numbers
05A15
11B37
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Summary:In this article, we define higher order Pell numbers. Then we introduce a new family of hyper complex numbers by using higher order Pell numbers. We call these families as the higher order Pell 2 s -ions. We present some algebraic properties of the higher order Pell 2 s -ions such as recurrence relation, Binet’s formula, generating function, exponential generating function, Vajda’s identity, Catalan’s identity, Cassini’s identity and d’Ocagne’s identity. Also we obtain the matrix representation of the higher order Pell 2 s -ions, and so prove Cassini’s identity as a new type.
ISSN:0971-3611
2367-2501
DOI:10.1007/s41478-023-00579-2