On the Mersenne and Mersenne-Lucas hybrinomial quaternions

Authors

  • E. Eser Erzincan Binali Yıldırım University, Turkey
  • B. Kuloglu Erzincan Binali Yıldırım University, Turkey
  • E. Ozcan Erzincan Binali Yıldırım University, Turkey

DOI:

https://doi.org/10.31926/but.mif.2023.3.65.1.10

Keywords:

Mersenne sequence, Mersenne polynomials, Mersenne-Lucas sequence, hybrinomial, quaternions

Abstract

In this paper, we introduce Mersenne and Mersenne-Lucas hybrinomial quaternions and present some of their properties. Some identities are derived for these polynomials. Furthermore, we give the Binet formulas, Catalan, Cassini, d’Ocagne identity and generating and exponential generating function of these hybrinomial quaternions.

Author Biographies

E. Eser, Erzincan Binali Yıldırım University, Turkey

Department of Mathematics, Faculty of Art and Sciences

B. Kuloglu, Erzincan Binali Yıldırım University, Turkey

Department of Mathematics, Graduate School of Natural and Applied Sciences, Yalnızbag Campus, 24100, Erzincan

E. Ozcan, Erzincan Binali Yıldırım University, Turkey

Department of Mathematics, Faculty of Arts and Sciences, Yalnızbag Campus, 24100

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Published

2023-07-03

Issue

Vol. 3(65) No. 1 (2023)

Section

MATHEMATICS