Results 51 to 60 of about 1,083 (122)

The sums of the reciprocals of Fibonacci polynomials and Lucas polynomials

, 2012
In this article, we consider infinite sums derived from the reciprocals of the Fibonacci polynomials and Lucas polynomials, and infinite sums derived from the reciprocals of the square of the Fibonacci polynomials and Lucas polynomials. Then applying the
Zhengang Wu, Wenpeng Zhang
semanticscholar   +1 more source

Generalized Chebyshev Polynomials

Discussiones Mathematicae - General Algebra and Applications, 2018
Let h(x) be a non constant polynomial with rational coefficients. Our aim is to introduce the h(x)-Chebyshev polynomials of the first and second kind Tn and Un. We show that they are in a ℚ-vectorial subspace En(x) of ℚ[x] of dimension n.
Abchiche Mourad, Belbachir Hacéne
doaj   +1 more source

Identities Arising from Binomial-Like Formulas Involving Divisors of Numbers

Annales Mathematicae Silesianae, 2023
In this article, we derive a great number of identities involving the ω function counting distinct prime divisors of a given number n. These identities also include Pochhammer symbols, Fibonacci and Lucas numbers and many more.
Gryszka Karol
doaj   +1 more source

A particular matrix and its relationships with Fibonacci numbers [PDF]

arXiv, 2002
Determinants and symmetric functions of the eigenvalues of matrices characterizing stochastic processes with indepedent increments. Relationships with Fibonacci numbers are derived.
arxiv  

Vieta-Pell and Vieta-Pell-Lucas polynomials

, 2013
In the present paper, we introduce the recurrence relation of Vieta-Pell and Vieta-Pell-Lucas polynomials. We obtain the Binet form and generating functions of Vieta-Pell and Vieta-Pell-Lucas polynomials and define their associated sequences.
D. Taşcı, Feyza Yalcin
semanticscholar   +1 more source

Generalizations of some identities involving the fibonacci numbers [PDF]

arXiv, 2003
In this paper we study the sum $$\sum_{j_1+j_2+...+j_d=n}\prod_{i=1}^d F_{k\cdot j_i},$$ where $d\geq2$ and $k\geq1$.
arxiv  

On the sum of the reciprocals of k-generalized Fibonacci numbers

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022
In this note, we that if {Fn(k)}n≥0{\left\{ {F_n^{\left( k \right)}} \right\}_{n \ge 0}} denotes the k-generalized Fibonacci sequence then for n ≥ 2 the closest integer to the reciprocal of ∑m≥n1/Fm(k)\sum\nolimits_{m \ge n} {1/F_m^{\left( k \right)}} is
Alahmadi Adel, Luca Florian
doaj   +1 more source

Arithmetic properties of q-Fibonacci numbers and q-Pell numbers [PDF]

arXiv, 2005
We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers.
arxiv  

A note on some binomial sums [PDF]

arXiv, 2006
Modifying an idea of E. Brietzke we give simple proofs for the recurrence relations of some sequences of binomial sums which have previously been obtained by other more complicated methods.
arxiv  

The regularized product of the Fibonacci numbers [PDF]

arXiv, 2006
The regularized product of the Fibonacci numbers is evaluated.
arxiv