@article{Babadağ2024, 
author = {Faik Babadağ and Ali Atasoy},
title = {On hyper-dual vectors and angles with Pell, Pell-Lucas numbers},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {11},
pages = {30655-30666},
keywords = {hyper-dual Pell number, hyper-dual Pell-Lucas number, hyper-dual Pell vector, hyper-dual angle},
url = {https://www.sciopen.com/article/10.3934/math.20241480},
doi = {10.3934/math.20241480},
abstract = {In this paper, we introduce two types of hyper-dual numbers with components including Pell and Pell-Lucas numbers. This novel approach facilitates our understanding of hyper-dual numbers and properties of Pell and Pell-Lucas numbers. We also investigate fundamental properties and identities associated with Pell and Pell-Lucas numbers, such as the Binet-like formulas, Vajda-like, Catalan-like, Cassini-like, and d'Ocagne-like identities. Furthermore, we also define hyper-dual vectors by using Pell and Pell-Lucas vectors and discuse hyper-dual angles. This extensionis not only dependent on our understanding of dual numbers, it also highlights the interconnectedness between integer sequences and geometric concepts.}
}