Hyperbolic Horadam hybrid functions

Efruz Özlem Mersin
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 2, Pages 389–401
DOI: 10.7546/nntdm.2023.29.2.389-401
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Authors and affiliations

Efruz Özlem Mersin
Department of Mathematics, Faculty of Science and Arts,
Aksaray University, Aksaray, Turkey

Abstract

The aim of this paper is to introduce the hybrid form of the hyperbolic Horadam function and to investigate some of its properties such as the generating function. Another aim is to define hyperbolic Horadam hybrid sine and cosine functions and their symmetrical forms. For newly defined functions, some properties such as the recursive relations, derivatives, Cassini and De Moivre type identities are examined. In addition, the quasi-sine Horadam hybrid function and three-dimensional Horadam hybrid spiral are defined.

Keywords

  • Hyperbolic functions
  • Hybrid numbers
  • Horadam numbers

2020 Mathematics Subject Classification

  • 11B37
  • 11B39
  • 11K31
  • 11Y55

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Manuscript history

  • Received: 18 November 2022
  • Revised: 10 May 2023
  • Accepted: 20 May 2023
  • Online First: 23 May 2023

Copyright information

Ⓒ 2023 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Cite this paper

Mersin, E. Ö. (2023). Hyperbolic Horadam hybrid functions. Notes on Number Theory and Discrete Mathematics, 29(2), 389-401, DOI: 10.7546/nntdm.2023.29.2.389-401.

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