@article{GÜL2025, 
author = {Kübra GÜL},
title = {On    3-parameter generalized quaternions with higher order Leonardo numbers components},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {11},
pages = {6789-6804},
keywords = {higher order Leonardo numbers, 3-parameter generalized quaternions, Binet-type formulas, generating functions},
url = {https://www.sciopen.com/article/10.3934/era.2025300},
doi = {10.3934/era.2025300},
abstract = {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.}
}