On generalized bicomplex k-Fibonacci numbers

Tülay Yağmur
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 4, Pages 123–133
DOI: 10.7546/nntdm.2019.25.4.123-133
Full paper (PDF, 166 Kb)

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Authors and affiliations

Tülay Yağmur
Department of Mathematics, University of Aksaray
68100 Aksaray, Turkey

Abstract

In this paper, we introduce the generalized bicomplex k-Fibonacci numbers. We also give the generating function and Binet’s formula for these numbers. In addition, we obtain some identities such as Honsberger, d’Ocagne’s, Catalan’s, and Cassini’s identities involving the generalized bicomplex k-Fibonacci numbers.

Keywords

• Fibonacci numbers
• k-Fibonacci numbers
• Bicomplex numbers
  Generalized bicomplex numbers
• Generalized bicomplex k-Fibonacci numbers

2010 Mathematics Subject Classification

• 11B37
• 11B39
• 11R52

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