Incomplete k-Pell, k-Pell-Lucas and Modified k-Pell Numbers

Catarino, Paula

doi:10.15672/hjms.20164518616

Cited by 8 publications

(10 citation statements)

References 20 publications

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“…These numbers are examples of a numbers defined by a recurrence relation of second order. It is well known that the modified k − Pell numbers { } , N k n n q ∈ is defined in [1] [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. In order to determine generating functions of modified k-Pell numbers, Gaussian modified Pell numbers, Bivariate Complex Fibonacci and Lucas Polynomials, modified Pell Polynomials and Gaussian modified Pell Polynomials, we use analytical means and series manipulation methods.…”

Section: Introductionmentioning

confidence: 99%

Generating Functions of Modified Pell Numbers and Bivariate Complex Fibonacci Polynomials

Boughaba¹,

Boussayoud²,

Boubellouta³

2019

TJANT

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Section: Introductionmentioning

confidence: 99%

Generating Functions of Modified Pell Numbers and Bivariate Complex Fibonacci Polynomials

Boughaba¹,

Boussayoud²,

Boubellouta³

2019

TJANT

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“…in [2]. Let c(x) and A(x), respectively, be the generating function of the sequence of the Catalan numbers {Cn} and any sequence {an}.…”

Section: Generating Functions Of Catalan Transforms For These Sequencesmentioning

confidence: 99%

“…The known Pell numbers have some applications in many branches of mathematics such as group theory, calculus, applied mathematics, linear algebra, etc. [2,3,4,6,8,16].…”

Section: Introductionmentioning

confidence: 99%

Catalan transform of the k-Pell, k-Pell–Lucas and modified k-Pell sequence

Taştan¹,

Özkan²

2021

NNTDM

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In this study, we present the Catalan transforms of the k-Pell sequence, the k-Pell–Lucas sequence and the Modified k-Pell sequence and examine the properties of the sequences. Then we apply the Hankel transform to the Catalan transforms of the k-Pell sequence, the Catalan transform of the k-Pell–Lucas sequence and the Catalan transform of the Modified k-Pell sequence. Also, we obtain the generating functions of the Catalan transform of the k-Pell sequence, k-Pell–Lucas sequence and Modified k-Pell sequence. Furthermore, we acquire an interesting characteristic related to the determinant of the Hankel transform of the sequences.

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“…Registramos a intensa produção de trabalhos em periódicos científicos que revelam os traços essenciais não apenas matemáticos mas, também, epistemológicos e evolutivos de determinadas classes de sequências recorrentes. Por outro lado, não podemos desconsiderar o caráter cifrado e demasiadamente restritivo de uma cultura matemática peculiarmente comunicada pelos periódicos e jornais especializados internacionais (Campos et all, 2014;Catarino, 2016;Catarino & Vasco, 2013;Catarino & Borges, 2020;Campos & Vasco, 2019).…”

Section: Cooperação E Pesquisa Brasil X Portugalunclassified

Uma Proposta De Investigação Histórico-Epistemológica Sobre Sequências Recorrentes De 2ª Ordem

Alves

Catarino

2020

PARADIGMA

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A formação de professores no Brasil não pode prescindir de um componente histórico-matemático e evolutivo. Nesse sentido, se torna imprescindível ao professor compreender a natureza intrinseca sobre o conhecimento matemático e seus processos ou itinerários de evolução e de irrefreável generalização. Dessa forma, o presente trabalho apresenta os dados preliminares de uma investigação amaparada pelos pressupostos de uma Engenharia Didática de Formação, em desenvolvimento no Brasil. O trabalho revela a uma importante cooperação científica envolvendo pesquisadores portugueses, sobre o asssunto de sequências recorrentes de 2ª ordem e aponta a contribuição de pesquisas desenvolvidas no período de 2015 – 2020, no Programa de Pós-graduação em Ensino de Ciências e Matemátca, do Instituto Federal de Educação, Ciências e Tecnologia do Estado do Ceará – IFCE. Por fim, o trabalho apresenta algns indicadores que devem demarcar um importante cenário para a formação (inicial e continuada) de professores no Brasil.Palavras-chave: História e Epistemologia da Matemática; Sequências recorrentes; Formação de Profesores de Matemática; Engenharia Didática de Formação.A PROPOSAL FOR HISTORICAL-EPISTEMOLOGICAL RESEARCH ON THE 2ND ORDER SEQUENCESAbstract. Teacher training in Brazil cannot do without a historical-mathematical and evolutionary component. In this sense, it is essential for the teacher to understand the intrinsic nature of mathematical knowledge and its processes or itineraries of evolution and irrepressible generalization. Thus, the present work presents the preliminary data of an investigation supported by the assumptions of Didactic Engineering of Training, under development in Brazil. The work reveals an important scientific cooperation involving Portuguese researchers, on the subject of recurrent 2nd order sequences and points out the contribution of research developed in the period 2015 - 2020, in the Postgraduate Program in Science Teaching and Mathematics, of the Institute Federal Institute of Education, Science and Technology of the State of Ceará - IFCE. Finally, the work presents some indicators that should outline an important scenario for the training (initial and continuing) of teachers in Brazil.Keywords: History and Epistemology of Mathematics; Recurring strings; Mathematics Teacher Training; Didactic Engineering Training.

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Incomplete k-Pell, k-Pell-Lucas and Modified k-Pell Numbers

Abstract: In this paper, it is dened the incomplete k-Pell, k-Pell-Lucas and Modied k-Pell numbers, it is studied the recurrence relations, some properties of these sequences of integers and their generating functions.

Cited by 8 publications

References 20 publications

Generating Functions of Modified Pell Numbers and Bivariate Complex Fibonacci Polynomials

Generating Functions of Modified Pell Numbers and Bivariate Complex Fibonacci Polynomials

Catalan transform of the k-Pell, k-Pell–Lucas and modified k-Pell sequence

Uma Proposta De Investigação Histórico-Epistemológica Sobre Sequências Recorrentes De 2ª Ordem

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