Un critére de transcendance de fractions continues dans [formula omitted

Abstract

There are uncountably many continued fractions of formal power series with bounded sequence of partial quotients, most of them are transcendental, but it is not very easy to give examples. This paper creates many families of such examples in an interesting way using the continued fractions of algebraic series with bounded partial quotients (none such are known and presumably do not exist for real numbers), given by Baum-Sweet, Mills-Robbins, Lasjaunias [continued fractions for certain algebraic formal power series over a finite field, Proceedings of the Sixth International Conference on Finite Fields and Applications, Oaxaca, Mexico, May 2001, Springer, Berlin, pp. 220–228], and recent many families by Thakur [J. Number Theory 59 (1996) 248–261; J. Number Theory 66 (1997) 129–147; J. Number Theory 79 (1999) 284–291].