On truncations of entire transcendental functions

In this paper it is shown that outside every circle, every finite value is assumed by some truncation of the Taylor series of an entire transcendental function (in fact, by every truncation of sufficiently high degree). This result differs from both Casorati-Weierstrass and Picard theorems inasmuch as the truncations actually assume the preassigned values and that there are no exceptional values.