From a quartic continued fraction in $\mathbb{F}_3((T^-1))$ to a transcendental continued fraction in $\mathbb{Q}((T^-1))$ through an infinite word over {1,2}
Résumé
We explicitly describe a noteworthy transcendental continued fraction in the field of power series over Q, having irrationality measure equal to 3. This continued fraction is a generating function of a particular sequence in the set {1, 2}. The origin of this sequence, whose study was initiated in a recent paper, is to be found in another continued fraction, in the field of power series over $\mathbb{F}_3$, which satisfies a simple algebraic equation of degree 4, introduced thirty years ago by D. Robbins.
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