On generalized Fibonacci and Lucas polynomials

Nalli, Ayse; Haukkanen, Pentti

doi:10.1016/j.chaos.2009.04.048

Cited by 79 publications

(55 citation statements)

References 17 publications

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“…In particular, the differential recurrence relations (2.6)-(2.9) are generalizations of Liu,[18, Lemmas 1 and 2, Equations (7), (9)- (11)] and the recurrence relation (2.10) is a generalization of Liu. [18, Theorem 1, Equation (12)] Among the recurrence relations and differential recurrence relations given in Theorems 2.2 and 2.3, Equations (2.5) and (2.10) may be the most important.…”

Section: )mentioning

confidence: 99%

Some results on convolved (p,q)-Fibonacci polynomials

Wang

2015

Integral Transforms and Special Functions

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In this paper, based on the (p, q)-Fibonacci polynomials u n (x) and (p, q)-Lucas polynomials v n (x), we introduce the convolved (p, q)-Fibonacci polynomials u (r) n (x), which generalize the convolved Fibonacci numbers, the convolved Pell polynomials, and the Gegenbauer polynomials. We give the expressions, expansions, recurrence relations and differential recurrence relations of u (r) n (x), and establish the relations between u (r) n (x), u n (x) and v n (x). Moreover, we also study the determinantal representations of u (r) n (x) and v n (x), and present an algebraic interpretation of the polynomials u (r) n (x).

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Section: )mentioning

confidence: 99%

Some results on convolved (p,q)-Fibonacci polynomials

Wang

2015

Integral Transforms and Special Functions

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“…, 1972;BICKNELL & HOGGATT, Jr., 1963;BICKNELL, 1965;ERCOLANO, 1976;HOGGAT. Jr. & BICKNELL, 1973;WALTON & HORADAM, 1971), como outras, de ordem bastantes atuais (BASU & DAS, 2014;NALLI, 2006;NALLI & HAUKKANEN, 2009;PRASAD, 2014), que indicam um vigor preservado do modelo de reprodução de pares de coelhos.…”

Section: Sobre a Evolução Do Modelo De Fibonacciunclassified

Sobre a evolução matemática, histórico-epistemológica do modelo de Fibonacci: sobre a abordagem matricial

Alves¹

2017

Revista Thema

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RESUMOEste artigo aborda uma temática que proporciona uma perspectiva epistemológica não estática, atinente a um tópico ou ramo ABSTRACTThis article discusses a theme that provides a non-static epistemological perspective relating to a specific topic or a mathematical branch that represents one particular approach that characterize the evolution, the generalization and the sistematization of a model proposed by Leonardo Fibonacci, in 1202. Its main scope is demarcate some elements that characterize the use of matrix model in order and resolution of old and recentes problems. Among the many aspects of the Theory of Fibonacci Numbers, the matrix approach allows the description of unexpected properties. Finally, the writting seeks to provide elements that allow for a investigative action, historical and epistemological order, in a initial training context of mathematics teacher. Moreover, surely the elements of historical and mathematical epistemological order are presented, troughout the text, in order to show contitute an essential part of initial teacher training formation.

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“…Since the algebra A 2 is a subalgebra of M 2 (C), one can naturally restrict the trace tr on M 2 (C) to that on A 2 . i.e., the pair (A 2 , tr) forms a noncommutative free probability space in the sense of [8] and [9].…”

Section: A Group Algebramentioning

confidence: 99%

Matricial Representations of Certain Finitely Presented Groups Generated by Order-2 Generators and Their Applications

Golden¹,

Cho²

2017

AJUR

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In this paper, we study matricial representations of certain finitely presented groups Γ 2 N with N -generators of order-2. As an application, we consider a group algebra A 2 of Γ 2 2 , under our representations. Specifically, we characterize the inverses g −1 of all group elements g in Γ 2 2 , in terms of matrices in the group algebra A 2 . From the study of this characterization, we realize there are close relations between the trace of the radial operator of A 2 , and the Lucas numbers appearing in the Lucas triangle.1991 Mathematics Subject Classification. 05A19, 30E50, 37E99, 44A60.

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On generalized Fibonacci and Lucas polynomials

Cited by 79 publications

References 17 publications

Some results on convolved (p,q)-Fibonacci polynomials

Some results on convolved (p,q)-Fibonacci polynomials

Sobre a evolução matemática, histórico-epistemológica do modelo de Fibonacci: sobre a abordagem matricial

Matricial Representations of Certain Finitely Presented Groups Generated by Order-2 Generators and Their Applications

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