| Title:
|
On Balancing and Lucas-balancing Quaternions (English) |
| Author:
|
Patel, Bijan Kumar |
| Author:
|
Ray, Prasanta Kumar |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
29 |
| Issue:
|
3 |
| Year:
|
2021 |
| Pages:
|
325-341 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this article is to investigate two new classes of quaternions, namely, balancing and Lucas-balancing quaternions that are based on balancing and Lucas-balancing numbers, respectively. Further, some identities including Binet's formulas, summation formulas, Catalan's identity, etc. concerning these quaternions are also established. (English) |
| Keyword:
|
Recurrence relations |
| Keyword:
|
Balancing numbers |
| Keyword:
|
Lucas-balancing numbers |
| Keyword:
|
Quaternions |
| MSC:
|
11B37 |
| MSC:
|
11B39 |
| MSC:
|
20G20 |
| idZBL:
|
Zbl 07484371 |
| idMR:
|
MR4355416 |
| . |
| Date available:
|
2022-01-10T09:57:24Z |
| Last updated:
|
2022-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149319 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Horadam, A.F.: Complex Fibonacci numbers and Fibonacci quaternions.The American Mathematical Monthly, 70, 3, 1963, 289-291, JSTOR, 10.2307/2313129 |
| Reference:
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| Reference:
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[10] Iyer, M.R.: A note on Fibonacci quaternions.Fibonacci Quarterly, 7, 3, 1969, 225-229, |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
