Hypercomplex numbers of the Fibonaci Type

Hypercomplex numbers of the Fibonacci type

Anetta Szynal-Liana, Iwona Włoch
     monografia
słowa kluczowe: quaternions, bicomplex numbers, hybrid numbers, hybrinomials, Fibonacci numbers
© Copyright by Oficyna Wydawnicza
Politechniki Rzeszowskiej, Rzeszów 2019
ISBN 978-83-7934-338-6


Contents
Notation
Preface
1    Hypercomplex numbers
1.1 Complex numbers
1.2 Quaternions
1.3 Octonions, sedenions and trigintaduonions
1.4 Tessarines and bicomplex numbers
1.5 Dual numbers, hyperbolic numbers and hybrid numbers
2    Numbers and polynomials of the Fibonacci type
2.1 A short history of numbers of the Fibonacci type
2.2 Binet formulas and generating functions
2.3 Binomial representations
2.4 The Fibonacci type identities
2.5 Matrix generators for numbers of the Fibonacci type
2.6 Fibonacci type polynomials
2.7 Generalizations
3    Quaternions of the Fibonacci type
3.1 Pell quaternions and Pell-Lucas quaternions
3.2 F(p; n)-Fibonacci quaternions and L(p; n)-Lucas quaternions
4     Bicomplex numbers of the Fibonacci type 63
4.1 Bicomplex Jacobsthal numbers
4.2 Generalized Fibonacci and Lucas bicomplex numbers
4.3 Matrix generators for generalized bicomplex Fibonacci and Lucas numbers
5    Hybrid numbers of the Fibonacci type
5.1 Horadam hybrid numbers
5.2 Balancing hybrid numbers
6     Hybrinomials of the Fibonacci type
6.1 Denition and basic properties
6.2 Fibonacci type hybrinomials identities
6.3 Matrix generator for hybrinomials
Conclusion remarks
Bibliography
Index
Appendix
List of Tables