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2025, Volume 33, Issue 11: 6789-6804. doi: 10.3934/era.2025300
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On $ 3 $-parameter generalized quaternions with higher order Leonardo numbers components

  • Department of Computer Engineering, Faculty of Engineering and Architecture, Kafkas University, Kars 36100, Turkey
  • Published: 17 November 2025

  • In this paper, a novel type of $ 3 $-parameter generalized quaternions ($ 3 $ -PGQs) is introduced, constructed from higher order Leonardo numbers and referred to as the higher order Leonardo $ 3 $-parameter generalized quaternions (shortly, higher order Leonardo $ 3 $-PGQs). Several fundamental properties of these quaternions are examined, including their recurrence relations, a Binet-type formula, and both generating and exponential generating functions. In addition, the obtained identities show that the higher order Leonardo $ 3 $-PGQs can be expressed in closed form in terms of Fibonacci numbers, Fibonacci generalized quaternions, and higher order Leonardo numbers.

    Citation: Kübra GÜL. On $ 3 $-parameter generalized quaternions with higher order Leonardo numbers components[J]. Electronic Research Archive, 2025, 33(11): 6789-6804. doi: 10.3934/era.2025300

    Related Papers:

  • In this paper, a novel type of $ 3 $-parameter generalized quaternions ($ 3 $ -PGQs) is introduced, constructed from higher order Leonardo numbers and referred to as the higher order Leonardo $ 3 $-parameter generalized quaternions (shortly, higher order Leonardo $ 3 $-PGQs). Several fundamental properties of these quaternions are examined, including their recurrence relations, a Binet-type formula, and both generating and exponential generating functions. In addition, the obtained identities show that the higher order Leonardo $ 3 $-PGQs can be expressed in closed form in terms of Fibonacci numbers, Fibonacci generalized quaternions, and higher order Leonardo numbers.



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