On the m-extension of the Fibonacci and Lucas p-numbers
| dc.contributor.author | Kocer, E. Gokcen | |
| dc.contributor.author | Tuglu, Naim | |
| dc.contributor.author | Stakhov, Alexey | |
| dc.date.accessioned | 2020-03-26T17:39:27Z | |
| dc.date.available | 2020-03-26T17:39:27Z | |
| dc.date.issued | 2009 | |
| dc.department | Selçuk Üniversitesi | en_US |
| dc.description.abstract | In this article, we define the m-extension of the Fibonacci and Lucas p-numbers (p >= 0 is integer and m >= 0 is real number) from which, specifying p and in, classic Fibonacci and Lucas numbers (p = 1, m = 1), Pell and Pell-Lucas numbers (p = 1, m = 2), Fibonacci and Lucas p-numbers (m = 1), Fibonacci in-numbers (p = 1), Pell and Pell-Lucas p-numbers (m = 2) are obtained. Afterwards, we obtain the continuous functions for the m-extension of the Fibonacci and Lucas p-numbers using the generalized Binet formulas. Also we introduce in the article a new class of mathematical constants - the Golden (p,m)-Proportions, which are a wide generalization of the classical golden mean, the golden p-proportions and the golden m-proportions. The article is of fundamental interest for theoretical physics where Fibonacci numbers and the golden mean are used widely. (c) 2007 Elsevier Ltd. All rights reserved. | en_US |
| dc.identifier.doi | 10.1016/j.chaos.2007.09.071 | en_US |
| dc.identifier.endpage | 1906 | en_US |
| dc.identifier.issn | 0960-0779 | en_US |
| dc.identifier.issn | 1873-2887 | en_US |
| dc.identifier.issue | 4 | en_US |
| dc.identifier.scopusquality | Q1 | en_US |
| dc.identifier.startpage | 1890 | en_US |
| dc.identifier.uri | https://dx.doi.org/10.1016/j.chaos.2007.09.071 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12395/23720 | |
| dc.identifier.volume | 40 | en_US |
| dc.identifier.wos | WOS:000266653500030 | en_US |
| dc.identifier.wosquality | Q1 | en_US |
| dc.indekslendigikaynak | Web of Science | en_US |
| dc.indekslendigikaynak | Scopus | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | PERGAMON-ELSEVIER SCIENCE LTD | en_US |
| dc.relation.ispartof | CHAOS SOLITONS & FRACTALS | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.selcuk | 20240510_oaig | en_US |
| dc.title | On the m-extension of the Fibonacci and Lucas p-numbers | en_US |
| dc.type | Article | en_US |
