Abstract
1. INTRODUCTION. According to Picard's 'great theorem', a transcendental (i.e., non-polynomial) entire function takes on every complex value, with one possible exception, infinitely many times in the complex plane. I will present here two theorems, related to Picard's theorem, whose proofs use only the techniques of a first course in complex analysis. They are weak versions of known results, weak enough (I hope) to be widely accessible, but still strong enough (I hope) to be interesting. 2. POWER SERIES WITH GAPS. From properties of the coefficients of a power series it is possible to deduce properties of the function represented by the series. For example, a power series is said to have 'gaps' if most of its coefficients vanish, and the existence of gaps implies information about the values taken on by the associated function. The following theorem illustrates this.
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