scholarly journals On the finite reciprocal sums of Fibonacci and Lucas polynomials

2019 ◽  
Vol 4 (6) ◽  
pp. 1569-1581
Author(s):  
Utkal Keshari Dutta ◽  
◽  
Prasanta Kumar Ray
Keyword(s):  
Lucas Polynomials ◽  
Reciprocal Sums

scholarly journals Composition Identities of Chebyshev Polynomials, via 2 × 2 Matrix Powers

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 746
Author(s):  
Primo Brandi ◽  
Paolo Emilio Ricci
Keyword(s):  
Chebyshev Polynomials ◽  
Representation Formula ◽  
Complex Matrices ◽  
Lucas Polynomials ◽  
Standard Composition

Starting from a representation formula for 2 × 2 non-singular complex matrices in terms of 2nd kind Chebyshev polynomials, a link is observed between the 1st kind Chebyshev polinomials and traces of matrix powers. Then, the standard composition of matrix powers is used in order to derive composition identities of 2nd and 1st kind Chebyshev polynomials. Before concluding the paper, the possibility to extend this procedure to the multivariate Chebyshev and Lucas polynomials is touched on.

scholarly journals Some Properties of the(p,q)-Fibonacci and(p,q)-Lucas Polynomials

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
GwangYeon Lee ◽  
Mustafa Asci
Keyword(s):  
Generating Functions ◽  
Combinatorial Identities ◽  
Fibonacci Polynomials ◽  
Lucas Polynomials ◽  
Pascal Matrix ◽  
Riordan Arrays ◽  
Combinatorial Sums

Riordan arrays are useful for solving the combinatorial sums by the help of generating functions. Many theorems can be easily proved by Riordan arrays. In this paper we consider the Pascal matrix and define a new generalization of Fibonacci polynomials called(p,q)-Fibonacci polynomials. We obtain combinatorial identities and by using Riordan method we get factorizations of Pascal matrix involving(p,q)-Fibonacci polynomials.

scholarly journals On the k -Lucas Numbers and Lucas Polynomials

2017 ◽  
Vol 5 (4) ◽  
pp. 121-125 ◽  
Author(s):  
Ali Boussayoud ◽  
Mohamed Kerada ◽  
Nesrine Harrouche
Keyword(s):  
Lucas Numbers ◽  
Lucas Polynomials

scholarly journals Algebraic relations for reciprocal sums of Fibonacci numbers

2007 ◽  
Vol 130 (1) ◽  
pp. 37-60 ◽  
Author(s):  
Carsten Elsner ◽  
Shun Shimomura ◽  
Iekata Shiokawa
Keyword(s):  
Fibonacci Numbers ◽  
Reciprocal Sums

scholarly journals Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers

1997 ◽  
Vol 73 (7) ◽  
pp. 140-142 ◽  
Author(s):  
Daniel Duverney ◽  
Keiji Nishioka ◽  
Kumiko Nishioka ◽  
Iekata Shiokawa
Keyword(s):  
Continued Fraction ◽  
Fibonacci Numbers ◽  
Reciprocal Sums

Transcendence of reciprocal sums of binary recurrences

2008 ◽  
Vol 157 (4) ◽  
pp. 323-334 ◽  
Author(s):  
Tomoaki Kanoko ◽  
Takeshi Kurosawa ◽  
Iekata Shiokawa
Keyword(s):  
Reciprocal Sums

scholarly journals Incomplete Bivariate Fibonacci and Lucas -Polynomials

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Dursun Tasci ◽  
Mirac Cetin Firengiz ◽  
Naim Tuglu
Keyword(s):  
Generating Function ◽  
Lucas Numbers ◽  
Lucas Polynomials ◽  
Fibonacci And Lucas Numbers

We define the incomplete bivariate Fibonacci and Lucas polynomials. In the case , , we obtain the incomplete Fibonacci and Lucas numbers. If , , we have the incomplete Pell and Pell-Lucas numbers. On choosing , , we get the incomplete generalized Jacobsthal number and besides for the incomplete generalized Jacobsthal-Lucas numbers. In the case , , , we have the incomplete Fibonacci and Lucas numbers. If , , , , we obtain the Fibonacci and Lucas numbers. Also generating function and properties of the incomplete bivariate Fibonacci and Lucas polynomials are given.

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