Some transcendental functions that yield transcendental values for every algebraic entry

A transcendental function usually yields a transcendental value for an algebraic entry belonging to its domain, the algebraic exceptions forming the so-called \emph{exceptional set}. For instance, the exceptional set of the function $\,\exp(z)\,$ is the unitary set $\{0\}$, which follows from the Hermite-Lindemann theorem. In this note, we give some explicit examples of transcendental entire functions having empty exceptional sets, i.e. functions that yield transcendental values for all algebraic entries, without exceptions.