On Bicomplex ( p,q )-Fibonacci Quaternions

Çağla Çelemoğlu ()
Additional contact information
Çağla Çelemoğlu: Department of Mathematics, Faculty of Science, Ondokuz Mayıs University, Samsun 55270, Turkey

Mathematics, 2024, vol. 12, issue 3, 1-18

Abstract: Here, we describe the bicomplex p , q -Fibonacci numbers and the bicomplex p , q -Fibonacci quaternions based on these numbers to show that bicomplex numbers are not defined the same as bicomplex quaternions. Then, we give some of their equations, including the Binet formula, generating function, Catalan, Cassini, and d’Ocagne’s identities, and summation formulas for both. We also create a matrix for bicomplex p , q -Fibonacci quaternions, and we obtain the determinant of a special matrix that gives the terms of that quaternion. With this study, we get a general form of the second-order bicomplex number sequences and the second-order bicomplex quaternions. In addition, we show that these two concepts, defined as the same in many studies, are different.

Keywords: ( p , q )-Fibonacci number; ( p , q )-Fibonacci quaternion; bicomplex Fibonacci number; generating function; Catalan identity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/3/461/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/3/461/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:3:p:461-:d:1330449

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().