Scholarlink

<p>In this study, we define the Parastichy Fibonacci and Parastichy Fibonacci-Lucas numbers. Also, we find basic properties of these numbers, such as characteristic equations and properties. Then we give the Binet formulas, special generating function, and special summation formulas. We associate the terms of the Parastichy Fibonacci and Parastichy Fibonacci-Lucas numbers with matrices. In addition, we calculate the Simson formulas of these numbers. Moreover, we examine the relationships among these numbers. We relate Parastichy Fibonacci numbers with special number sequences such as Lucas numbers. Furthermore, we obtain important correlations between Parastichy Fibonacci and Parastichy Fibonacci-Lucas numbers. We explore the use of generalized Parastichy Fibonacci numbers in the context of hyperbolic quaternions. For these hyperbolic quaternions, we derive various properties, including generating functions and summation formulas. Finally, we establish a relationship between the terms of the Parastichy Fibonacci and Parastichy Fibonacci-Lucas numbers and their associated hyperbolic quaternion values.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Generalized Parastichy Fibonacci Numbers and Their Applications

  • 期刊论文

  • 发表日期：

    2026年3月30日

查看全文
  • Hakan Akkuş,
  • Anthony G. Shannon,
  • Engin Özkan

摘要

In this study, we define the Parastichy Fibonacci and Parastichy Fibonacci-Lucas numbers. Also, we find basic properties of these numbers, such as characteristic equations and properties. Then we give the Binet formulas, special generating function, and special summation formulas. We associate the terms of the Parastichy Fibonacci and Parastichy Fibonacci-Lucas numbers with matrices. In addition, we calculate the Simson formulas of these numbers. Moreover, we examine the relationships among these numbers. We relate Parastichy Fibonacci numbers with special number sequences such as Lucas numbers. Furthermore, we obtain important correlations between Parastichy Fibonacci and Parastichy Fibonacci-Lucas numbers. We explore the use of generalized Parastichy Fibonacci numbers in the context of hyperbolic quaternions. For these hyperbolic quaternions, we derive various properties, including generating functions and summation formulas. Finally, we establish a relationship between the terms of the Parastichy Fibonacci and Parastichy Fibonacci-Lucas numbers and their associated hyperbolic quaternion values.