Displaying similar documents to “Conjugate sequences in a Fibonacci-Lucas sense and some identities for sums of powers of their elements.”

Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences

Roman Wituła, Damian Słota (2006)

Open Mathematics

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In this paper some decompositions of Cauchy polynomials, Ferrers-Jackson polynomials and polynomials of the form x 2n + y 2n , n ∈ ℕ, are studied. These decompositions are used to generate the identities for powers of Fibonacci and Lucas numbers as well as for powers of the so called conjugate recurrence sequences. Also, some new identities for Chebyshev polynomials of the first kind are presented here.

Some boundedness results for systems of two rational difference equations

Gabriel Lugo, Frank Palladino (2010)

Open Mathematics

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We study k th order systems of two rational difference equations x n = α + ∑ i = 1 k β i x n - 1 + ∑ i = 1 k γ i y n - 1 A + ∑ j = 1 k B j x n - j + ∑ j = 1 k C j y n - j , y n = p + ∑ i = 1 k δ i x n - i + ∑ i = 1 k ε i y n - i q + ∑ j = 1 k D j x n - j + ∑ j = 1 k E j y n - j n ∈ ℕ . In particular, we assume non-negative parameters and non-negative initial conditions, such that the denominators are nonzero. We develop several approaches which allow us to extend well known boundedness results on the k th order rational difference equation to the setting of systems in certain cases.