Lacunary value

In complex analysis, a subfield of mathematics, a lacunary value or gap of a complex-valued function defined on a subset of the complex plane is a complex number which is not in the image of the function.{{citation|title=Dictionary of Analysis, Calculus, and Differential Equations|volume=1|series=Comprehensive dictionary of mathematics|editor-first=Douglas N.|editor-last=Clark|publisher=CRC Press|year=1999|isbn=9780849303203|pages=97–98|url=https://books.google.com/books?id=jQL4ZU4RjPYC&pg=PA97}}.

More specifically, given a subset X of the complex plane C and a function f : X → C, a complex number z is called a lacunary value of f if z ∉ image(f).

Note, for example, that 0 is the only lacunary value of the complex exponential function. The two Picard theorems limit the number of possible lacunary values of certain types of holomorphic functions.