IJPAM: Volume 34, No. 2 (2007)

GENERATING MATRICES FOR FIBONACCI,
LUCAS AND SPECIAL ORTHOGONAL
POLYNOMIALS WITH ALGORITHMS

Mustafa Asci$^1$, Bayram Çekim$^2$, Dursun Tasci$^3$
$^{1,2,3}$Department of Mathematics
Faculty of Sciences and Arts
University of Gazi
Teknikokullar, Ankara, 06500, TURKEY
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]
$^3$e-mail: [email protected]


Abstract.In this paper we get the Fibonacci polynomials for special cases of Sturm Liouville boundary value problems. We show the orthogonallity of Fibonacci polynomials. In Section 3 by using the definition of $n\times n$ Hessenberg matrices we give the generating matrices of the Fiboniacci and Lucas polynomials and for the special orthogonal polynomials. In the last section we give two algorithms for finding the Fibonacci and Lucas polynomials.

Received: November 2, 2006

AMS Subject Classification: 15A15, 11B39, 15A36

Key Words and Phrases: Fibonacci polynomial, Sturm Liouville algorithm

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 34
Issue: 2