Affiliation:
1. Institute of Mathematics, Federal University of Mato Grosso do Sul, Campo Grande 79074-460, Brazil
2. Department of Mathematics, University of Trás-os-Montes e Alto Douro, 5001-801 Vila Real, Portugal
Abstract
Many different number systems have been the topic of research. One of the recently studied number systems is that of hybrid numbers, which are generalizations of other number systems. In this work, we introduce and study the hybrid hyper k-Pell, hybrid hyper k-Pell–Lucas, and hybrid hyper Modified k-Pell numbers. In order to study these new sequences, we established new properties, generating functions, and the Binet formula of the hyper k-Pell, hyper k-Pell–Lucas, and hyper Modified k-Pell sequences. Thus, we present some algebraic properties, recurrence relations, generating functions, the Binet formulas, and some identities for the hybrid hyper k-Pell, hybrid hyper k-Pell–Lucas, and hybrid hyper Modified k-Pell numbers.
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
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