2025/10/03 by Gamaliel Morales, Morales, Gamaliel
Physics and Astronomy · Mathematics · #Advanced Mathematical Theories and Applications #Algebraic and Geometric Analysis #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2510.15931
Recently, Kuloğlu \it et al. \citeKul introduced the higher order Horadam numbers. In this study, novel 3-parameter generalized quaternion sequences of higher order Horadam numbers, which have not been studied before, are defined by investigating the relationship between generalized quaternions, which are important mathematical objects used in physics and mathematics, and higher order Horadam quaternions, which are extensions of the higher order Horadam numbers to quaternion algebra. Also, the recurrence relations of sequences whose members are higher order Horadam 3-parameter generalized quaternions are described. Furthermore, certain properties of these generalized quaternions are presented, such as the generating and exponential function, summation and Binet formula, and some identities resulting from these quaternions are obtained.