Continued fractions for quadratic elements in formal power series (Q409032)

\textit{W. M. Schmidt} [Acta Arith. 95, No. 2, 139--166 (2000; Zbl 0987.11041)] showed that for a field \(k\) of characteristic \(0\), there exists a quadratic element in \(k((t^{-1}))\) whose continued fraction is not psedoperiodic. In this paper, the authors give examples of continued fraction expansions that are not psedoperiodic for some quadratic elements in \(\mathbb Q((t^{-1}))\). They also give a conjecture related to the continued fraction expansions of quadratic elements in \(\mathbb Q((t^{-1}))\).