Construction of dual-generalized complex Fibonacci and Lucas quaternions
Gülsüm Yeliz Şentürk, Nurten Gürses, Sali̇m Yüce
Abstract
The aim of this paper is to construct dual-generalized complex Fibonacci and Lucas quaternions. It examines the properties both as dual-generalized complex number and as quaternion. Additionally, general recurrence relations, Binet's formulas, Tagiuri's (or Vajda's like), Honsberger's, d'Ocagne's, Cassini's and Catalan's identities are obtained. A series of matrix representations of these special quaternions is introduced. Finally, the multiplication of dual-generalized complex Fibonacci and Lucas quaternions are also expressed as their different matrix representations.
Topics & Concepts
QuaternionFibonacci numberLucas numberMathematicsDual (grammatical number)Fibonacci polynomialsDual quaternionConstruct (python library)Algebra over a fieldMatrix (chemical analysis)Recurrence relationPure mathematicsLucas sequenceArithmeticCombinatoricsComputer scienceLinguisticsGeometryOrthogonal polynomialsComposite materialPhilosophyProgramming languageMaterials scienceDifference polynomialsAdvanced Mathematical Theories and ApplicationsMathematics and ApplicationsAdvanced Mathematical Theories