Abstract
Let beta is an element of F-q((x(-1))) be a quadratic Pisot unit formal power series such that deg(beta) = 2 and let F is an element of F-q (x, beta). It is shown in [4] that f has a finite continued. beta-fraction or an infinite continued. beta-fraction finished by polynomials of the form A(n) = alpha(n)x + delta(n,) alpha(n,) delta(n) is an element of F-q. In this paper we give a study of the depth of the continued. - fraction denoted by Psi(beta)(F)