the characteristic polynomial of a symmetric matrix M . Many instances of Coxeter polynomials f A (T ), for A a finite dimensional algebra, are (graphically) representable. We study the case of extended canonical algebras A, see [11], show that the corresponding polynomials f A (T ) are representable and satisfy a Chebysheff type recursion formula. We get consequences for the eigenvalues of the Coxeter transformation of A showing, for instance, that at most four eigenvalues may lie outside the unit circle.