holomorphic
Complex-differentiable on an open set around every point in its domainComplex-differentiable on an open set around every point in its domain.
» Holomorphic functions have several agreeable properties, making them easy to work with.
Meaning
2 senses(not comparable)Complex-differentiable on an open set around every point in its domain.
1998, Robert Friedman, Algebraic Surfaces and Holomorphic Vector Bundles, Springer, page 303, A holomorphic 1-form on X is closed, and so 0=dη₁=df and η₂.
holomorph
голоморфныйgolomorfnyj
(not comparable)Having holohedral symmetry.
Examples
5 sentencesHolomorphic functions have several agreeable properties, making them easy to work with.
If a holomorphic function has an infinite sequence of zeroes with an accumulation point, then it is identically zero.
A holomorphic function can be expressed as a convergent power series in a neighborhood of any point in its domain.
If two holomorphic functions with the same domain agree at infinitely many points in a bounded set, then they are identical.
If you can show directly that this function's complex derivatives exist everywhere in its domain, then you can conclude that it's holomorphic.
Translations
5 languagesBy meaning 1
By meaning 1
Origin
From holo- + -morphic.From holo- + -morphic.
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