EJMT Abstract

Different approaches are known for the introduction of the classical Chebyshev polynomials. Although mostly they are introduced in connection with trigonometric identities or defined as orthogonal polynomials or a solution of a particular differential equation, we take extremality as a defining property. We discuss the current computer tools which make the exploration of extremal polynomials possibly more easy and enjoyable. Finally we investigate ways to generalize the notion of classical Chebyshev polynomials as extremal polynomials which are less known. The author used the general computer algebra system Mathematica for the development, but other systems can be also suitbale for the exploration: a part of a GeoGebra book as an illustrative example is also included.