Vol. 14, No. 2, 2021

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Some remarks on generalized recursive polynomials

Luke Wiljanen and Aklilu Zeleke

Vol. 14 (2021), No. 2, 181–194
Abstract

We generate Fibonacci-type recursive polynomials through continued fractions. These polynomials generalize the well-known Fibonacci and Lucas polynomials. We present several results such as generating functions, finite sum representations and identities satisfied by these polynomials. Analytic results about the zeros of these polynomials are also presented.

Keywords
generalized Fibonacci polynomials, matrix identities, generating functions
Mathematical Subject Classification 2010
Primary: 11B39
Milestones
Received: 8 May 2019
Revised: 10 June 2020
Accepted: 5 December 2020
Published: 6 April 2021

Communicated by Kenneth S. Berenhaut
Authors
Luke Wiljanen
Department of Mathematics
Michigan State University
East Lansing, MI
United States
Aklilu Zeleke
Lyman Briggs College and Department of Statistics and Probability
Michigan State University
East Lansing, MI
United States