Properties of hyperbolic generalized Pell numbers

Yüksel Soykan and Melih Göcen
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310-5132, Online ISSN 2367-8275
Volume 26, 2020, Number 4, Pages 136—153
DOI: 10.7546/nntdm.2020.26.4.136-153
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Authors and affiliations

Yüksel Soykan
Department of Mathematics, Zonguldak Bülent Ecevit University
67100, Zonguldak, Turkey

Melih Göcen
Department of Mathematics, Zonguldak Bülent Ecevit University
67100, Zonguldak, Turkey

Abstract

In this paper, we introduce the generalized hyperbolic Pell numbers over the bidimensional Clifford algebra of hyperbolic numbers. As special cases, we deal with hyperbolic Pell and hyperbolic Pell–Lucas numbers. We present Binet’s formulas, generating functions and the summation formulas for these numbers. Moreover, we give Catalan’s, Cassini’s, d’Ocagne’s, Gelin–Cesàro’s, Melham’s identities and present matrices related to these sequences.

Keywords

  • Pell numbers
  • Pell–Lucas numbers
  • Hyperbolic numbers
  • Hyperbolic Pell numbers
  • Cassini identity.

2010 Mathematics Subject Classification

  • 11B39
  • 11B83

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Cite this paper

Soykan, Y., & Göcen, M. (2020). Properties of hyperbolic generalized Pell numbers. Notes on Number Theory and Discrete Mathematics, 26 (4), 136-153, doi: 10.7546/nntdm.2020.26.4.136-153.

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