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Öğe BINOMIAL IDENTITIES INVOLVING THE GENERALIZED FIBONACCI TYPE POLYNOMIALS(CHARLES BABBAGE RES CTR, 2011) Kilic, Emrah; Irmak, NurettinWe present some binomial identities for sums of the bivariate Fibonacci polynomials and for weighted sums of the usual Fibonacci polynomials with indices in arithmetic progression.Öğe Binomial identities involving the generalized fibonacci type polynomials(Charles Babbage Research Centre, 2011) Kilic, Emrah; Irmak, NurettinWe present some binomial identities for sums of the bivariate Fibonacci polynomials and for weighted sums of the usual Fibonacci polynomials with indices in arithmetic progression.Öğe Decompositions of the Cauchy and Ferrers-Jackson polynomials(UNIV OSIJEK, DEPT MATHEMATICS, 2016) Irmak, Nurettin; Kilic, EmrahRecently, Witula and Slota have given decompositions of the Cauchy and Ferrers-Jackson polynomials [Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences, Central Europan J. Math., 2006]. Our main purpose is to derive a different decomposition of the Cauchy and Ferrers-Jackson polynomials. Our approach is to use the Waring formula and the Saalschutz identity to prove the claimed results. Also, we obtain generalizations of the results of Carlitz, Hunter and Koshy as corollaries of our results about sums and differences of powers of the Fibonacci and Lucas numbers.Öğe Reciprocal sums of l-th power of generalized binary sequences with indices(CHARLES BABBAGE RES CTR, 2008) Kilic, Emrah; Irmak, NurettinRecently in [5], the author considered certain reciprocal sums of general second order recurrence {W-n}. In this paper, we generalize the results of Xi and we give some new results for the reciprocal sums of l-th power of general second order recurrence {W-kn} for arbitrary positive integer k.
