On Quaternions with Higher Order Jacobsthal Numbers Components

IF 1 Q3 MULTIDISCIPLINARY SCIENCES

gazi university journal of science Pub Date : 2023-03-01 DOI:10.35378/gujs.1002454

Engin ÖZKAN, Mine UYSAL

引用次数: 1

Abstract

In this study, we present higher order Jacobsthal numbers. Then we define higher order Jacobsthal quaternions by using higher order Jacobsthal numbers. We give the concept of the norm and conjugate for these quaternions. We express and prove some propositions related to these quaternions. Also, we find the recurrence relation, the Binet formula and the generating function for these quaternions. Finally, we calculate Cassini, Catalan, Vajda and d’Ocagne identities for higher order Jacobsthal quaternions.

查看原文本刊更多论文

具有高阶jacobthal数分量的四元数

在本研究中，我们提出了高阶jacobthal数。然后用高阶雅各布数定义了高阶雅各布四元数。我们给出了这些四元数的范数和共轭的概念。我们表达并证明了与这些四元数有关的一些命题。并给出了这些四元数的递推关系、Binet公式和生成函数。最后，我们计算了高阶jacobthal四元数的Cassini, Catalan, Vajda和d 'Ocagne恒等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

gazi university journal of science MULTIDISCIPLINARY SCIENCES-

CiteScore

1.60

自引率

11.10%

发文量

期刊介绍： The scope of the “Gazi University Journal of Science” comprises such as original research on all aspects of basic science, engineering and technology. Original research results, scientific reviews and short communication notes in various fields of science and technology are considered for publication. The publication language of the journal is English. Manuscripts previously published in another journal are not accepted. Manuscripts with a suitable balance of practice and theory are preferred. A review article is expected to give in-depth information and satisfying evaluation of a specific scientific or technologic subject, supported with an extensive list of sources. Short communication notes prepared by researchers who would like to share the first outcomes of their on-going, original research work are welcome.