标题： 关于高阶Horadam三参数广义四元数 显示英文标题

标题： On higher order Horadam 3-parameter generalized quaternions

摘要： 最近，Kuloğlu {\it 等} \cite{Kul} 引入了高阶Horadam数。 在本研究中，通过研究重要的数学对象——广义四元数与高阶Horadam四元数之间的关系，定义了尚未被研究过的高阶Horadam数的新型三参数广义四元数序列，这些高阶Horadam四元数是将高阶Horadam数扩展到四元数代数的结果。 此外，还描述了其成员为高阶Horadam三参数广义四元数的序列的递推关系。 此外，还介绍了这些广义四元数的一些性质，例如生成函数和指数函数、求和和Binet公式，并得到了由此四元数产生的某些恒等式。 显示英文摘要

摘要： Recently, Kulo\u{g}lu {\it et al.} \cite{Kul} 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.