Some transcendental functions with an empty exceptional set

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A transcendental function usually returns transcendental values at algebraic points. The (algebraic) exceptions form the so-called exceptional set, as for instance the unitary set {0} for the function f(z) = eᶻ, according to the Hermite-Lindemann theorem. In this note, we give some explicit examples of transcendental entire functions whose exceptional set are empty.