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.[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.

References

Clark, Douglas N., ed. (1999), Dictionary of Analysis, Calculus, and Differential Equations, Comprehensive dictionary of mathematics, vol. 1, CRC Press, pp. 97–98, ISBN 9780849303203.

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[1] Clark, Douglas N., ed. (1999), Dictionary of Analysis, Calculus, and Differential Equations, Comprehensive dictionary of mathematics, vol. 1, CRC Press, pp. 97–98, ISBN 9780849303203.