Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences |
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Authors: | Roman Wituła Damian Słota |
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Affiliation: | (1) Institute of Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland |
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Abstract: | 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. |
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Keywords: | Cauchy polynomials Ferrers-Jackson polynomials Chebyshev polynomials Fibonacci and Lucas numbers recurrence sequences |
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