New summation identities of hyperbolic k-Fibonacci and k-Lucas quaternions

A. D. Godase
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 31, 2025, Number 3, Pages 570–582
DOI: 10.7546/nntdm.2025.31.3.570-582
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Authors and affiliations

A. D. Godase
Department of Mathematics, V. P. College Vaijapur
Aurangabad, 423701, Maharashtra, India

Abstract

In this paper, we introduce a set of identities involving hyperbolic k-Fibonacci quaternions and k-Lucas quaternions. Moreover, we derive summation identities for hyperbolic k-Fibonacci and k-Lucas quaternions by utilizing established properties of k-Fibonacci and k-Lucas numbers. These findings add valuable insight into the relationships between these quaternion sequences and offer valuable insights into their properties.

Keywords

  • Fibonacci quaternion
  • Lucas quaternion
  • k-Fibonacci quaternion
  • k-Lucas quaternion

2020 Mathematics Subject Classification

  • 11B39
  • 11B37
  • 11B52

References

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Manuscript history

  • Received: 27 February 2025
  • Revised: 6 August 2025
  • Accepted: 17 August 2025
  • Online First: 22 August 2025

Copyright information

Ⓒ 2025 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

Godase, A. D. (2025). New summation identities of hyperbolic k-Fibonacci and k-Lucas quaternions. Notes on Number Theory and Discrete Mathematics, 31(3), 570-582, DOI: 10.7546/nntdm.2025.31.3.570-582.

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