On Analyticity and Holomorphicity

A complex function is analytic if and only if it is holomorphic. Because of this equivalence, an analytic function in the complex case is often defined to be one that is holomorphic, instead of one having a Taylor series as above. Although the two definitions are equivalent, it is not an easy matter to prove their equivalence, and a reader who does not yet have this result available will have to pay attention as to which definition of analytic is being used.

"analytic" is owned by djao.

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Other names:

real analytic, real analytic function, complex analytic, complex analytic function, analytic function

Attachments:: infinitely-differentiable function that is not analytic (Example) by ariels
existence of power series (Result) by rmilson
zeroes of analytic functions are isolated (Result) by brianbirgen

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Cross-references: equivalent, definitions, complex, equivalence, holomorphic, complex function, neighborhood, open, converges, point, Taylor series, function, real numbers, complex numbers, domain
There are 140 references to this entry.

This is version 5 of analytic, born on 2001-12-28, modified 2004-10-24.
Object id is 1147, canonical name is Analytic.
Accessed 19691 times total.

Classification:

AMS MSC:	30B10 (Functions of a complex variable :: Series expansions :: Power series )
	26A99 (Real functions :: Functions of one variable :: Miscellaneous)

Pending Errata and Addenda

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