Gaussian-bihyperbolic Numbers Containing Pell and Pell-Lucas Numbers
In this study, we define a new type of Pell and Pell-Lucas numbers which are called Gaussian-bihyperbolic Pell and Pell-Lucas numbers. We also define negaGaussian-bihyperbolic Pell and Pell-Lucas numbers. Moreover, we obtain Binet’s formulas, generating function formulas, d’Ocagne’s identities, Cata...
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| Format: | Article |
| Language: | English |
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Çanakkale Onsekiz Mart University
2023-03-01
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| Series: | Journal of Advanced Research in Natural and Applied Sciences |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/2403058 |
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| author | Hasan Gökbaş |
| author_facet | Hasan Gökbaş |
| author_sort | Hasan Gökbaş |
| collection | DOAJ |
| description | In this study, we define a new type of Pell and Pell-Lucas numbers which are called Gaussian-bihyperbolic Pell and Pell-Lucas numbers. We also define negaGaussian-bihyperbolic Pell and Pell-Lucas numbers. Moreover, we obtain Binet’s formulas, generating function formulas, d’Ocagne’s identities, Catalan’s identities, Cassini’s identities and some sum formulas for these new type numbers and we investigate some algebraic proporties of these. Furthermore, we give the matrix representation of Gaussian-bihyperbolic Pell and Pell-Lucas numbers. |
| format | Article |
| id | doaj-art-00ad8786f5844641b9077cffb1aaefc9 |
| institution | Kabale University |
| issn | 2757-5195 |
| language | English |
| publishDate | 2023-03-01 |
| publisher | Çanakkale Onsekiz Mart University |
| record_format | Article |
| series | Journal of Advanced Research in Natural and Applied Sciences |
| spelling | doaj-art-00ad8786f5844641b9077cffb1aaefc92025-02-05T17:57:35ZengÇanakkale Onsekiz Mart UniversityJournal of Advanced Research in Natural and Applied Sciences2757-51952023-03-019118318910.28979/jarnas.1110421453Gaussian-bihyperbolic Numbers Containing Pell and Pell-Lucas NumbersHasan Gökbaş0https://orcid.org/0000-0002-3323-8205Bitlis EREN ÜniversitesiIn this study, we define a new type of Pell and Pell-Lucas numbers which are called Gaussian-bihyperbolic Pell and Pell-Lucas numbers. We also define negaGaussian-bihyperbolic Pell and Pell-Lucas numbers. Moreover, we obtain Binet’s formulas, generating function formulas, d’Ocagne’s identities, Catalan’s identities, Cassini’s identities and some sum formulas for these new type numbers and we investigate some algebraic proporties of these. Furthermore, we give the matrix representation of Gaussian-bihyperbolic Pell and Pell-Lucas numbers.https://dergipark.org.tr/en/download/article-file/2403058bihyperbolicgaussian-bihyperbolicgaussian-bihyperbolic pellgaussian-bihyperbolic pell-lucas |
| spellingShingle | Hasan Gökbaş Gaussian-bihyperbolic Numbers Containing Pell and Pell-Lucas Numbers Journal of Advanced Research in Natural and Applied Sciences bihyperbolic gaussian-bihyperbolic gaussian-bihyperbolic pell gaussian-bihyperbolic pell-lucas |
| title | Gaussian-bihyperbolic Numbers Containing Pell and Pell-Lucas Numbers |
| title_full | Gaussian-bihyperbolic Numbers Containing Pell and Pell-Lucas Numbers |
| title_fullStr | Gaussian-bihyperbolic Numbers Containing Pell and Pell-Lucas Numbers |
| title_full_unstemmed | Gaussian-bihyperbolic Numbers Containing Pell and Pell-Lucas Numbers |
| title_short | Gaussian-bihyperbolic Numbers Containing Pell and Pell-Lucas Numbers |
| title_sort | gaussian bihyperbolic numbers containing pell and pell lucas numbers |
| topic | bihyperbolic gaussian-bihyperbolic gaussian-bihyperbolic pell gaussian-bihyperbolic pell-lucas |
| url | https://dergipark.org.tr/en/download/article-file/2403058 |
| work_keys_str_mv | AT hasangokbas gaussianbihyperbolicnumberscontainingpellandpelllucasnumbers |