  It is widely believed that the continued fraction expansion of every
irrational algebraic number $\alpha$ either is eventually periodic (and we know
that this is the case if and only if $\alpha$ is a quadratic irrational), or it
contains arbitrarily large partial quotients. Apparently, this question was
first considered by Khintchine. A preliminary step towards its resolution
consists in providing explicit examples of transcendental continued fractions.
The main purpose of the present work is to present new families of
transcendental continued fractions with bounded partial quotients. Our results
are derived thanks to new combinatorial transcendence criteria recently
obtained by Adamczewski and Bugeaud.
