Some remarks on generalized recursive polynomials

Wiljanen, Luke; Zeleke, Aklilu

doi:10.2140/involve.2021.14.181

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Some remarks on generalized recursive polynomials

Luke Wiljanen and Aklilu Zeleke

Vol. 14 (2021), No. 2, 181–194

DOI: 10.2140/involve.2021.14.181

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

Vol. 14, No. 2, 2021