Abstract
Let F-q((X-1)) be the field of formal power series in X-1 over F-q, the field with q elements. Let f is an element of F-q((X-1)) satisfy the irreducible polynomial Af(2) + Bf + C = 0, with Delta = B-2 - 4AC. Let Per(f) be the length of the period of the continued fraction expansion of f. In this article, we show that Per (f) <= (q - 1)(2 root q)(deg Delta-2). We also prove that F Q is a monic polynomial with even degree, then the length of the period of the continued fraction expansion of any square root of Q is less than (q - 1) (2 root q)(degQ-1)).