On a family of continued fractions in $Q((T^1))$ associated to infinite binary words derived from the Thue-Morse sequence

Bill Allombert, Alain Lasjaunias

For each integer n > 1, we present an element in $Q((T^{-}1))$, having a power series expansion based on an infinite word W(n), over the alphabet ${+1;-1}g and whose continued fracti…