Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers
In this paper, we define a new sequence called the quaternion-type Catalan sequence and give generating function, exponential representation, quaternionic Catalan matrix and its some properties. Then, we introduce a quaternion-type Catalan transform, which is a generalization of the Catalan transfor...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/2439110 |
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| author | Kübra Gül |
| author_facet | Kübra Gül |
| author_sort | Kübra Gül |
| collection | DOAJ |
| description | In this paper, we define a new sequence called the quaternion-type Catalan sequence and give generating function, exponential representation, quaternionic Catalan matrix and its some properties. Then, we introduce a quaternion-type Catalan transform, which is a generalization of the Catalan transform, and its inverse. Moreover, we apply the quaternion-type Catalan transforms to ρ-Fibonacci and ρ-Lucas sequences and derive some new sequences by using these quaternion-type Catalan transforms. |
| format | Article |
| id | doaj-art-c9933c076bcc4161a08bc81252a14b3b |
| institution | DOAJ |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-c9933c076bcc4161a08bc81252a14b3b2025-08-20T03:23:59ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/2439110Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas NumbersKübra Gül0Department of Computer EngineeringIn this paper, we define a new sequence called the quaternion-type Catalan sequence and give generating function, exponential representation, quaternionic Catalan matrix and its some properties. Then, we introduce a quaternion-type Catalan transform, which is a generalization of the Catalan transform, and its inverse. Moreover, we apply the quaternion-type Catalan transforms to ρ-Fibonacci and ρ-Lucas sequences and derive some new sequences by using these quaternion-type Catalan transforms.http://dx.doi.org/10.1155/2023/2439110 |
| spellingShingle | Kübra Gül Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers Journal of Mathematics |
| title | Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers |
| title_full | Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers |
| title_fullStr | Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers |
| title_full_unstemmed | Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers |
| title_short | Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers |
| title_sort | quaternion type catalan transforms of the ρ fibonacci and ρ lucas numbers |
| url | http://dx.doi.org/10.1155/2023/2439110 |
| work_keys_str_mv | AT kubragul quaterniontypecatalantransformsoftherfibonacciandrlucasnumbers |