On the m-extension of the Fibonacci and Lucas p-numbers
Küçük Resim Yok
Tarih
2009
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
PERGAMON-ELSEVIER SCIENCE LTD
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
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.
Açıklama
Anahtar Kelimeler
Kaynak
CHAOS SOLITONS & FRACTALS
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
40
Sayı
4
