Lacunary value

Lacunary value

In mathematics, more precisely in complex analysis, a lacunary value 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.

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.


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