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On higher order Fibonacci hyper complex numbers
- Source :
- Chaos, Solitons & Fractals. 148:111044
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
Abstract
- This paper deals with developing a new class of quaternions, octonions and sedenions called higher order Fibonacci 2 m -ions (or-higher order Fibonacci hyper complex numbers) whose components are higher order Fibonacci numbers. We give recurrence relation, Binet formula, generating function and exponential generating function of higher order Fibonacci 2 m -ions. We also derive some identities such as Vajda’s identity, Catalan’s identity, Cassini’s identity, and d’Ocagne’s identity with the aid of the Binet formula. Finally, we develop some matrix identities involving higher order Fibonacci 2 m -ions which allow us to obtain some properties of these higher order hyper complex numbers.
- Subjects :
- Recurrence relation
Fibonacci number
General Mathematics
Applied Mathematics
Generating function
General Physics and Astronomy
Sedenion
Order (ring theory)
Statistical and Nonlinear Physics
01 natural sciences
010305 fluids & plasmas
Combinatorics
Identity (mathematics)
Matrix (mathematics)
0103 physical sciences
010301 acoustics
Complex number
Mathematics
Subjects
Details
- ISSN :
- 09600779
- Volume :
- 148
- Database :
- OpenAIRE
- Journal :
- Chaos, Solitons & Fractals
- Accession number :
- edsair.doi...........925c84a22717174256d39f28fe5d3bb3