| 21. | A holomorphic function whose domain is the whole complex plane is called an entire function.
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| 22. | All holomorphic functions are complex-analytic.
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| 23. | So informally one might say that poles occur as reciprocals of zeros of holomorphic functions.
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| 24. | The main point of Riemann surfaces is that holomorphic functions may be defined between them.
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| 25. | Moreover, any antiholomorphic function can be obtained in this manner from a holomorphic function.
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| 26. | Here \ mathcal O ( X ) denotes the ring of holomorphic functions on X.
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| 27. | Often, a complex domain serves as the domain of definition for a holomorphic function.
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| 28. | The classical definition of Hardy space is of holomorphic functions on ? with this property.
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| 29. | Holomorphic functions exhibit some remarkable features.
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| 30. | More generally, Laurent series can be used to express holomorphic functions defined on an disc.
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