Diophantine approximation and continued fraction expansion for quartic power series over F3

The main contribution of this paper is providing families of examples conjecturally generalizing the almost unique known so far example introduced first by Mills and Robbins (J Number Theory 23:388-404, 1986) of quartic power series over F-3(T) having an approximation exponent equal to 2 in relation with Roth's theorem as proved by Lasjaunias (J Number Theory 65:206-224 1997), and having a continued fraction expansion with an unbounded sequence of partial quotients.