One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers
In this paper, we introduce one-parameter generalization of dual-hyperbolic Jacobsthal numbers – dual-hyperbolic r-Jacobsthal numbers. We present some properties of them, among others the Binet formula, Catalan, Cassini, and d’Ocagne identities. Moreover, we give the generating function and summatio...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2023-09-01
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| Series: | Annales Mathematicae Silesianae |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/amsil-2023-0005 |
| _version_ | 1827807998052925440 |
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| author | Bród Dorota Szynal-Liana Anetta Włoch Iwona |
| author_facet | Bród Dorota Szynal-Liana Anetta Włoch Iwona |
| author_sort | Bród Dorota |
| collection | DOAJ |
| description | In this paper, we introduce one-parameter generalization of dual-hyperbolic Jacobsthal numbers – dual-hyperbolic r-Jacobsthal numbers. We present some properties of them, among others the Binet formula, Catalan, Cassini, and d’Ocagne identities. Moreover, we give the generating function and summation formula for these numbers. The presented results are a generalization of the results for the dual-hyperbolic Jacobsthal numbers. |
| first_indexed | 2024-03-11T22:06:00Z |
| format | Article |
| id | doaj.art-888d7236da3542f0920bc170a65b4f50 |
| institution | Directory Open Access Journal |
| issn | 2391-4238 |
| language | English |
| last_indexed | 2024-03-11T22:06:00Z |
| publishDate | 2023-09-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annales Mathematicae Silesianae |
| spelling | doaj.art-888d7236da3542f0920bc170a65b4f502023-09-25T06:06:48ZengSciendoAnnales Mathematicae Silesianae2391-42382023-09-0137222423910.2478/amsil-2023-0005One-Parameter Generalization of Dual-Hyperbolic Jacobsthal NumbersBród Dorota0Szynal-Liana Anetta1Włoch Iwona21Rzeszow University of Technology, The Faculty of Mathematics and Applied Physics, al. Powstańców Warszawy 12 35-959RzeszówPoland1Rzeszow University of Technology, The Faculty of Mathematics and Applied Physics, al. Powstańców Warszawy 12 35-959RzeszówPoland1Rzeszow University of Technology, The Faculty of Mathematics and Applied Physics, al. Powstańców Warszawy 12 35-959RzeszówPolandIn this paper, we introduce one-parameter generalization of dual-hyperbolic Jacobsthal numbers – dual-hyperbolic r-Jacobsthal numbers. We present some properties of them, among others the Binet formula, Catalan, Cassini, and d’Ocagne identities. Moreover, we give the generating function and summation formula for these numbers. The presented results are a generalization of the results for the dual-hyperbolic Jacobsthal numbers.https://doi.org/10.2478/amsil-2023-0005jacobsthal numbersdual-hyperbolic numbersdual-hyperbolic jacobsthal numbersbinet formulacatalan identitycassini identity11b3711b39 |
| spellingShingle | Bród Dorota Szynal-Liana Anetta Włoch Iwona One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers Annales Mathematicae Silesianae jacobsthal numbers dual-hyperbolic numbers dual-hyperbolic jacobsthal numbers binet formula catalan identity cassini identity 11b37 11b39 |
| title | One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers |
| title_full | One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers |
| title_fullStr | One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers |
| title_full_unstemmed | One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers |
| title_short | One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers |
| title_sort | one parameter generalization of dual hyperbolic jacobsthal numbers |
| topic | jacobsthal numbers dual-hyperbolic numbers dual-hyperbolic jacobsthal numbers binet formula catalan identity cassini identity 11b37 11b39 |
| url | https://doi.org/10.2478/amsil-2023-0005 |
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