New formulas including convolution, connection and radicals formulas of k-Fibonacci and k-Lucas polynomials

W. M. Abd-Elhameed () and N. A. Zeyada
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W. M. Abd-Elhameed: Cairo University
N. A. Zeyada: Cairo University

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 4, 1006-1016

Abstract: Abstract This paper is dedicated to deriving some new formulas of the two classes of polynomials, namely k-Fibonacci and k-Lucas polynomials. New connection formulas between these two classes are developed. We show that the connection coefficients are expressed explicitly in terms of hypergeometric functions of the type $$_2F_{1}(z)$$ 2 F 1 ( z ) , for certain z. Some linearization formulas of the two classes of polynomials are also given. New convolution identities involving the derivatives of the two classes of k-Fibonacci and k-Lucas polynomials are derived. As an important application of employing the two classes of polynomials, reduction formulas of some odd radicals are established.

Keywords: k-Fibonacci polynomials; k-Lucas polynomials; Connection and linearization problems; Reduction of radicals; Convolution identities (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00214-5

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