Results 91 to 100 of about 7,865 (225)

On the finite reciprocal sums of Fibonacci and Lucas polynomials

open access: yesAIMS Mathematics, 2019
In this note, we consider the finite reciprocal sums of Fibonacci and Lucas polynomials and derive some identities involving these sums.
Utkal Keshari Dutta, Prasanta Kumar Ray
doaj   +1 more source

Sums of powers of Fibonacci polynomials [PDF]

open access: yesProceedings - Mathematical Sciences, 2009
Using the explicit (Binet) formula for the Fibonacci polynomials, a summation formula for powers of Fibonacci polynomials is derived straightforwardly, which generalizes a recent result for squares that appeared in Proc. Ind. Acad. Sci. (Math. Sci.) 118 (2008) 27–41.
openaire   +1 more source

A numerical method to solve fractional Fredholm-Volterra integro-differential equations

open access: yesAlexandria Engineering Journal, 2023
The Goolden ratio is famous for the predictability it provides both in the microscopic world as well as in the dynamics of macroscopic structures of the universe. The extension of the Fibonacci series to the Fibonacci polynomials gives us the opportunity
Antonela Toma, Octavian Postavaru
doaj  

Derivations and Identitites for Fibonacci and Lucas Polynomials

open access: yesThe Fibonacci Quarterly, 2013
We introduce the notion of Fibonacci and Lucas derivations of the polynomial algebras and prove that any element of kernel of the derivations defines a polynomial identity for the Fibonacci and Lucas polynomials. Also, we prove that any polynomial identity for Appel polynomial yields a polynomial identity for the Fibonacci and Lucas polynomials and ...
openaire   +2 more sources

Fibonacci Operational Matrix Algorithm For Solving Differential Equations Of Lane-Emden Type

open access: yesSakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2019
The aim of this study is presentan effective and correct technique for solving differential equations ofLane-Emden type as initial value problems. In this work, a numerical method namedas the Fibonacci polynomial approximation method, for the approximate
Musa Çakmak
doaj   +1 more source

Generalizations of the Fibonacci and Lucas polynomials [PDF]

open access: yesFilomat, 2009
In this note we consider two sequences of polynomials, which are denoted by {Un(k),m} and {Vn(k),m}, where k, m, n are nonnegative integers, and m ? 2. These sequences represent generalizations of the well-known Fibonacci and Lucas polynomials. For example, if m = 2, then we obtain exactly the Fibonacci and Lucas polynomials. If m = 3, then polynomials
openaire   +2 more sources

Combined Pseudo-Random Sequence Generator for Cybersecurity. [PDF]

open access: yesSensors (Basel), 2022
Maksymovych V   +5 more
europepmc   +1 more source

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