On Convolved Fibonacci Polynomials

Waleed Mohamed Abd-Elhameed, Omar Mazen Alqubori and Anna Napoli ()
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Waleed Mohamed Abd-Elhameed: Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
Omar Mazen Alqubori: Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23831, Saudi Arabia
Anna Napoli: Department of Mathematics and Computer Science, University of Calabria, 87036 Rende, Italy

Mathematics, 2024, vol. 13, issue 1, 1-25

Abstract: This work delves deeply into convolved Fibonacci polynomials (CFPs) that are considered generalizations of the standard Fibonacci polynomials. We present new formulas for these polynomials. An expression for the repeated integrals of the CFPs in terms of their original polynomials is given. A new approach is followed to obtain the higher-order derivatives of these polynomials from the repeated integrals formula. The inversion and moment formulas for these polynomials, which we find, are the keys to developing further formulas for these polynomials. The derivatives of the moments of the CFPs in terms of their original polynomials and different symmetric and non-symmetric polynomials are also derived. New product formulas of these polynomials with some polynomials, including the linearization formulas of these polynomials, are also deduced. Some closed forms for definite and weighted definite integrals involving the CFPs are found as consequences of some of the introduced formulas.

Keywords: Fibonacci polynomials; generalized polynomials; recurrence formulas; linearization and connection coefficients; definite integrals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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