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Title: Decompositions of the Cauchy and Ferrers-Jackson polynomials
Authors: Irmak, Nurettin
Kılıç, Emrah
Keywords: Cauchy polynomial
Ferrers-Jackson polynomial
Fibonacci numbers
Lucas numbers
Issue Date: 2016
Publisher: Udruga Matematicara Osijek
Source: Irmak, N., & Kılıç, E. (2016). Decompositions of the Cauchy and Ferrers-Jackson polynomials. Mathematical Communications, 21(2), 163-170.
Abstract: Recently, 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.
ISSN: 1331-0623
Appears in Collections:Matematik Bölümü / Department of Mathematics
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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