Sums of powers of Fibonacci and Lucas polynomials in terms of Fibopolynomials

Pita-Ruiz, Claudio

Sums of powers of Fibonacci and Lucas polynomials in terms of Fibopolynomials

Journal

Annales Mathematicae et Informaticae

ISSN

1787-5021

Date Issued

2013

Author(s)

Pita-Ruiz, Claudio

Facultad de Ingeniería - CampCM

Type

text::journal::journal article

URL

https://scripta.up.edu.mx/handle/20.500.12552/4680

Abstract

We study sums of powers of Fibonacci and Lucas polynomials of the form and ∑qn=0Lktsn, where s,t,k are given natural numbers, together with the corresponding alternating sums ∑qn=0(−1)nFktsn(x) and ∑qn=0(−1)nLktsn(x). We give sufficient conditions on the parameters s,t,k for express these sums as linear combinations of certain s-Fibopolynomials.