PICARD VALUES OF MEROMORPHIC FUNCTIONS

The theorem of Picard in its simplest form asserts that every nonconstant functionf (z), meromorphic in the plane, assumes there all complex values w with the possible exception of two. A value w which is not assumed by f(z) will be called a Picard value. The problem of our paper concerns the possible relationships between Picard values of f(z) and its derivatives. Let us first consider integral functions. Here the complete result is the following, due to Milloux [2], though special cases go back to Saxer [4]. THEOREM A. If f(z) is a transcendental integral function, then either f(z) assumes every finite value infinitely often, or every derivative of f(z) assumes every finite value except possibly zero infinitely often. On the other hand the function eaz+b, when a # 0, has zero as a Picard value together with all its derivatives. The more general class of functions