Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences
In this paper, we define bi-periodic (p,q)-Fibonacci and bi-periodic (p,q)-Lucas sequences, which generalize Fibonacci type, Lucas type, bi-periodic Fibonacci type and bi-periodic Lucas type sequences, using recurrence relations of (p,q)-Fibonacci and (p,q)-Lucas sequences. Generating functions and...
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| Format: | Article |
| Language: | English |
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Sakarya University
2023-02-01
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| Series: | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/2556896 |
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| author | Yasemin Taşyurdu Naime Şeyda Türkoğlu |
| author_facet | Yasemin Taşyurdu Naime Şeyda Türkoğlu |
| author_sort | Yasemin Taşyurdu |
| collection | DOAJ |
| description | In this paper, we define bi-periodic (p,q)-Fibonacci and bi-periodic (p,q)-Lucas sequences, which generalize Fibonacci type, Lucas type, bi-periodic Fibonacci type and bi-periodic Lucas type sequences, using recurrence relations of (p,q)-Fibonacci and (p,q)-Lucas sequences. Generating functions and Binet formulas that allow us to calculate the nth terms of these sequences are given and the convergence properties of their consecutive terms are examined. Also, we prove some fundamental identities of bi-periodic (p,q)-Fibonacci and bi-periodic (p,q)-Lucas sequences conform to the well-known properties of Fibonacci and Lucas sequences. |
| format | Article |
| id | doaj-art-8c4a2a7899df4b6a9c7fc5c82c283531 |
| institution | Kabale University |
| issn | 2147-835X |
| language | English |
| publishDate | 2023-02-01 |
| publisher | Sakarya University |
| record_format | Article |
| series | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
| spelling | doaj-art-8c4a2a7899df4b6a9c7fc5c82c2835312024-12-23T08:14:25ZengSakarya UniversitySakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi2147-835X2023-02-0127111310.16984/saufenbilder.114861828Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas SequencesYasemin Taşyurdu0https://orcid.org/0000-0002-9011-8269Naime Şeyda Türkoğlu1https://orcid.org/0000-0003-2301-3958ERZINCAN BINALI YILDIRIM UNIVERSITYERZINCAN BINALI YILDIRIM UNIVERSITYIn this paper, we define bi-periodic (p,q)-Fibonacci and bi-periodic (p,q)-Lucas sequences, which generalize Fibonacci type, Lucas type, bi-periodic Fibonacci type and bi-periodic Lucas type sequences, using recurrence relations of (p,q)-Fibonacci and (p,q)-Lucas sequences. Generating functions and Binet formulas that allow us to calculate the nth terms of these sequences are given and the convergence properties of their consecutive terms are examined. Also, we prove some fundamental identities of bi-periodic (p,q)-Fibonacci and bi-periodic (p,q)-Lucas sequences conform to the well-known properties of Fibonacci and Lucas sequences.https://dergipark.org.tr/tr/download/article-file/2556896bi-periodic fibonacci numbersfibonacci numbergeneralized fibonacci numbersbi-periodic lucas numberslucas number |
| spellingShingle | Yasemin Taşyurdu Naime Şeyda Türkoğlu Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi bi-periodic fibonacci numbers fibonacci number generalized fibonacci numbers bi-periodic lucas numbers lucas number |
| title | Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences |
| title_full | Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences |
| title_fullStr | Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences |
| title_full_unstemmed | Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences |
| title_short | Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences |
| title_sort | bi periodic p q fibonacci and bi periodic p q lucas sequences |
| topic | bi-periodic fibonacci numbers fibonacci number generalized fibonacci numbers bi-periodic lucas numbers lucas number |
| url | https://dergipark.org.tr/tr/download/article-file/2556896 |
| work_keys_str_mv | AT yasemintasyurdu biperiodicpqfibonacciandbiperiodicpqlucassequences AT naimeseydaturkoglu biperiodicpqfibonacciandbiperiodicpqlucassequences |