IJPAM: Volume 53, No. 4 (2009)
FIBONACCI-LIKE POLYNOMIALS: COMPUTATIONAL
EXPERIMENTS, PROOFS, AND CONJECTURES
EXPERIMENTS, PROOFS, AND CONJECTURES
Sergei Abramovich
, Gennady A. Leonov
School of Education and Professional Studies
State University of New York
44, Potsdam Pierrepont Ave., Potsdam, NY 13676-2294, USA
e-mail: abramovs@potsdam.edu
Faculty of Mathematics and Mechanics
St. Petersburg State University
Universitetskyi, 28, Peterhof, St. Petersburg, 198504, RUSSIA
e-mail: leonov@math.spbu.ru
, Gennady A. Leonov
School of Education and Professional Studies
State University of New York
44, Potsdam Pierrepont Ave., Potsdam, NY 13676-2294, USA
e-mail: abramovs@potsdam.edu
Faculty of Mathematics and Mechanics
St. Petersburg State University
Universitetskyi, 28, Peterhof, St. Petersburg, 198504, RUSSIA
e-mail: leonov@math.spbu.ru
Abstract.This article introduces a new class of
polynomials arising in a course of exploring a qualitative
behavior of orbits of a two-parametric difference equation. The
use of symbolic computations and computational experiments in the
context of Maple made it possible to prove polynomial
generalizations of Cassini's identity for Fibonacci numbers and
formulate conjectures about polynomial forms of Catalan's
identity.
Received: May 9, 2009
AMS Subject Classification: 12-04, 11C08
Key Words and Phrases: Fibonacci-like polynomials, Cassini's identity, Catalan's identity, Maple
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 4