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On the range of universal functions. (English) Zbl 1023.30003
Summary: We examine the range of universal Taylor series. We prove that every universal Taylor series on the unit disc assumes every complex number, with one possible exception, infinitely often. On the other hand, we prove that on any simply connected domain there exist universal functions that omit one value.

30B10 Power series (including lacunary series) in one complex variable
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