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- Q207476 subject Q7009779.
- Q207476 abstract "In mathematics, holomorphic functions are the central objects of study in complex analysis. A holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain. The existence of a complex derivative in a neighborhood is a very strong condition, for it implies that any holomorphic function is actually infinitely differentiable and equal to its own Taylor series.The term analytic function is often used interchangeably with "holomorphic function", although the word “analytic” is also used in a broader sense to describe any function (real, complex, or of more general type) that can be written as a convergent power series in a neighborhood of each point in its domain. The fact that all holomorphic functions are complex analytic functions, and vice versa, is a major theorem in complex analysis.Holomorphic functions are also sometimes referred to as regular functions or as conformal maps. A holomorphic function whose domain is the whole complex plane is called an entire function. The phrase "holomorphic at a point z0" means not just differentiable at z0, but differentiable everywhere within some neighborhood of z0 in the complex plane.".
- Q207476 thumbnail Conformal_map.svg?width=300.
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- Q207476 type Thing.
- Q207476 comment "In mathematics, holomorphic functions are the central objects of study in complex analysis. A holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.".
- Q207476 label "Holomorphic function".
- Q207476 depiction Conformal_map.svg.