| Title:
|
On generalized bihyperbolic third-order Jacobsthal polynomials (English) |
| Author:
|
Cerda-Morales, Gamaliel |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
150 |
| Issue:
|
3 |
| Year:
|
2025 |
| Pages:
|
393-403 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A new generalization of third-order Jacobsthal bihyperbolic polynomials is introduced. Some of the properties of presented polynomials are given. A general Vajda formula for the generalized bihyperbolic third-order Jacobsthal polynomials is obtained. This result implies the Catalan, Cassini and d'Ocagne identities. Moreover, generating function and matrix generators for these polynomials are presented. (English) |
| Keyword:
|
third-order Jacobsthal number |
| Keyword:
|
hyperbolic number |
| Keyword:
|
bihyperbolic number |
| Keyword:
|
recurrence relation |
| MSC:
|
11B37 |
| MSC:
|
11B39 |
| DOI:
|
10.21136/MB.2024.0037-24 |
| . |
| Date available:
|
2025-09-26T14:31:38Z |
| Last updated:
|
2025-09-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153083 |
| . |
| Reference:
|
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| Reference:
|
[2] Bilgin, M., Ersoy, S.: Algebraic properties of bihyperbolic numbers.Adv. Appl. Clifford Algebr. 30 (2020), Article ID 13, 17 pages. Zbl 1442.30049, MR 4054825, 10.1007/s00006-019-1036-2 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[6] Cerda-Morales, G.: Dual third-order Jacobsthal quaternions.Proyecciones 37 (2018), 731-747. Zbl 1440.11015, MR 3882525, 10.4067/S0716-09172018000400731 |
| Reference:
|
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| Reference:
|
[8] Cockle, J.: On certain functions resembling quaternions, and on a new imaginary in algebra.Phil. Mag. (3) 33 (1848), 435-439. 10.1080/14786444808646139 |
| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| . |
