We prove that a formal power series in 1/x, whose coefficients are in a field extension ofQand are algebraically independent overQ, is differentially transcendental (i.e. not differentially algebraic) over this field extension. This is stated without proof in [2]. This result provides a source of functions analytic at ∞ that are not differentially algebraic overR. Such functions are of particular interest, because their germs belong to Hardy fields, but not to the classEof [1]-the intersection of all maximal Hardy fields.