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On Bicomplex (p,q)-Fibonacci Quaternions
Version 1
: Received: 18 December 2023 / Approved: 19 December 2023 / Online: 19 December 2023 (11:51:04 CET)
A peer-reviewed article of this Preprint also exists.
Çelemoğlu, Ç. On Bicomplex (p,q)-Fibonacci Quaternions. Mathematics 2024, 12, 461. Çelemoğlu, Ç. On Bicomplex (p,q)-Fibonacci Quaternions. Mathematics 2024, 12, 461.
Abstract
Here, we describe the bicomplex (p,q)- Fibonacci numbers and the bicomplex (p,q)- Fibonacci quaternions that are based on these numbers and give some of their equations, including the Binet formula, generating function, Catalan, Cassini, d’Ocagne’s identities, and some summation formulas for both of them. Finally, we create a matrix for bicomplex (p,q)- Fibonacci quaternions, and we obtain a determinant of a special matrix that gives the terms of that quaternion.
Keywords
p,q- Fibonacci number; p,q- Fibonacci quaternion; bicomplex fibonacci number; generating function; catalan identity
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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