Pauli Gaussian Fibonacci and Pauli Gaussian Lucas Quaternions
We have investigated new Pauli Fibonacci and Pauli Lucas quaternions by taking the components of these quaternions as Gaussian Fibonacci and Gaussian Lucas numbers, respectively. We have calculated some basic identities for these quaternions. Later, the generating functions and Binet formulas are ob...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/24/4655 |
| _version_ | 1827637940741734400 |
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| author | Ayşe Zeynep Azak |
| author_facet | Ayşe Zeynep Azak |
| author_sort | Ayşe Zeynep Azak |
| collection | DOAJ |
| description | We have investigated new Pauli Fibonacci and Pauli Lucas quaternions by taking the components of these quaternions as Gaussian Fibonacci and Gaussian Lucas numbers, respectively. We have calculated some basic identities for these quaternions. Later, the generating functions and Binet formulas are obtained for Pauli Gaussian Fibonacci and Pauli Gaussian Lucas quaternions. Furthermore, Honsberger’s identity, Catalan’s and Cassini’s identities have been given for Pauli Gaussian Fibonacci quaternions. |
| first_indexed | 2024-03-09T16:07:45Z |
| format | Article |
| id | doaj.art-10f4a0330a91431cbfcfdc4d4d792827 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T16:07:45Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-10f4a0330a91431cbfcfdc4d4d7928272023-11-24T16:27:25ZengMDPI AGMathematics2227-73902022-12-011024465510.3390/math10244655Pauli Gaussian Fibonacci and Pauli Gaussian Lucas QuaternionsAyşe Zeynep Azak0Faculty of Education, Mathematics and Science Education Department, Sakarya University, Sakarya 54300, TurkeyWe have investigated new Pauli Fibonacci and Pauli Lucas quaternions by taking the components of these quaternions as Gaussian Fibonacci and Gaussian Lucas numbers, respectively. We have calculated some basic identities for these quaternions. Later, the generating functions and Binet formulas are obtained for Pauli Gaussian Fibonacci and Pauli Gaussian Lucas quaternions. Furthermore, Honsberger’s identity, Catalan’s and Cassini’s identities have been given for Pauli Gaussian Fibonacci quaternions.https://www.mdpi.com/2227-7390/10/24/4655Pauli matrixPauli quaternionFibonacci quaternionPauli Gaussian Fibonacci quaternionPauli Gaussian Lucas quaternion |
| spellingShingle | Ayşe Zeynep Azak Pauli Gaussian Fibonacci and Pauli Gaussian Lucas Quaternions Mathematics Pauli matrix Pauli quaternion Fibonacci quaternion Pauli Gaussian Fibonacci quaternion Pauli Gaussian Lucas quaternion |
| title | Pauli Gaussian Fibonacci and Pauli Gaussian Lucas Quaternions |
| title_full | Pauli Gaussian Fibonacci and Pauli Gaussian Lucas Quaternions |
| title_fullStr | Pauli Gaussian Fibonacci and Pauli Gaussian Lucas Quaternions |
| title_full_unstemmed | Pauli Gaussian Fibonacci and Pauli Gaussian Lucas Quaternions |
| title_short | Pauli Gaussian Fibonacci and Pauli Gaussian Lucas Quaternions |
| title_sort | pauli gaussian fibonacci and pauli gaussian lucas quaternions |
| topic | Pauli matrix Pauli quaternion Fibonacci quaternion Pauli Gaussian Fibonacci quaternion Pauli Gaussian Lucas quaternion |
| url | https://www.mdpi.com/2227-7390/10/24/4655 |
| work_keys_str_mv | AT aysezeynepazak pauligaussianfibonacciandpauligaussianlucasquaternions |