entire function

Noun

Meaning

English Wikipedia has an article on:entire functionWikipedia
entire function (plural entire functions)

(mathematics) Any function of a complex variable that is holomorphic throughout the complex plane

Examples

In particular, if the real part is given on any curve in the complex plane where the real part of some other entire function is zero, then any multiple of that function can be added to the function we are trying to determine. Source: Internet

Similarly, a non-constant, entire function that does not hit a particular value will hit every other value an infinite number of times. Source: Internet

This is an example of Picard's little theorem that any non-constant entire function takes on every complex number as value with at most one value excepted. Source: Internet

If an entire function f(z) has a root at w, then f(z)/(z−w) is an entire function. Source: Internet

If a sequence of polynomials all of whose roots are real converges in a neighborhood of the origin to a limit which is not identically equal to zero, then this limit is an entire function. Source: Internet

Liouville's theorem states that any bounded entire function must be constant. Source: Internet

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