| Title:
|
On dual and hyper-dual $k$-Leonardo numbers (English) |
| Author:
|
Yağmur, Tülay |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0011-4642 |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
151 |
| Issue:
|
4 |
| Year:
|
2026 |
| Pages:
|
521-535 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We describe new classes of dual and hyper-dual numbers whose coefficients consist of the $k$-Leonardo numbers. We will call these numbers dual $k$-Leonardo numbers and hyper-dual $k$-Leonardo numbers, respectively. Then we examine several fundamental properties associated with the dual and hyper-dual $k$-Leonardo numbers, including recurrence relations, Binet-like formula, ordinary generating function, exponential generating function, and some identities such as Catalan and d'Ocagne. (English) |
| Keyword:
|
dual numbers |
| Keyword:
|
hyper-dual numbers |
| Keyword:
|
Leonardo numbers |
| Keyword:
|
$k$-Leonardo numbers |
| MSC:
|
11B37 |
| MSC:
|
11B39 |
| MSC:
|
11B83 |
| MSC:
|
11R52 |
| DOI:
|
10.21136/MB.2025.0036-25 |
| . |
| Date available:
|
2026-09-23T08:21:43Z |
| Last updated:
|
2026-09-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153764 |
| . |
| Reference:
|
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| Reference:
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| . |
