Novel Results for Two Generalized Classes of Fibonacci and Lucas Polynomials and Their Uses in the Reduction of Some Radicals

Waleed Mohamed Abd-Elhameed, Andreas N. Philippou and Nasr Anwer Zeyada
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Waleed Mohamed Abd-Elhameed: Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
Andreas N. Philippou: Department of Mathematics, University of Patras, 26504 Patras, Greece
Nasr Anwer Zeyada: Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt

Mathematics, 2022, vol. 10, issue 13, 1-18

Abstract: The goal of this study is to develop some new connection formulae between two generalized classes of Fibonacci and Lucas polynomials. Hypergeometric functions of the kind 2 F 1 ( z ) are included in all connection coefficients for a specific z . Several new connection formulae between some famous polynomials, such as Fibonacci, Lucas, Pell, Fermat, Pell–Lucas, and Fermat–Lucas polynomials, are deduced as special cases of the derived connection formulae. Some of the introduced formulae generalize some of those existing in the literature. As two applications of the derived connection formulae, some new formulae linking some celebrated numbers are given and also some newly closed formulae of certain definite weighted integrals are deduced. Based on using the two generalized classes of Fibonacci and Lucas polynomials, some new reduction formulae of certain odd and even radicals are developed.

Keywords: generalized Fibonacci and generalized Lucas numbers; Lucas and Fibonacci numbers; recurrence relation; radicals reduction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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