Mathematics Faculty Articles

Title

Numerical Results on the Zeros of Generalized Fibonacci Polynomials

Document Type

Article

Publication Date

1-1-1997

Publication Title

Calcolo: A Quarterly on Numerical Analysis and Theory of Computation

ISSN

0008-0624

Volume

34

Issue/No.

1-4

First Page

25

Last Page

40

Abstract

We study some fundamental properties of generalized Fibonacci polynomials, by using the properties and characteristics of classical Fibonacci polynomials as a motivation. We derive the generating function and an explicit representation of these polynomials. A trace relation for a related r×r matrix Q r is derived. We then study the location and distribution of the zeros of the polynomials by illustrating our numerical results and by means of the so-called Newton sum rules.

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