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.
[1] 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.
This mathematical analysis–related article is a stub.