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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-4785 |