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

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## Details

### 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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## Cite this paper

Yağmur, T. (2019). On generalized bicomplex *k*-Fibonacci numbers. Notes on Number Theory and Discrete Mathematics, 25(4), 123-133, doi: 10.7546/nntdm.2019.25.4.123-133.