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residue (Definition)

Let $ U \subset \mathbb{C}$ be a domain and let $ f: U \longrightarrow \mathbb{C}$ be a function represented by a Laurent series

$\displaystyle f(z) := \sum_{k=-\infty}^\infty c_k (z-a)^k $
centered about $ a$. The coefficient $ c_{-1}$ of the above Laurent series is called the residue of $ f$ at $ a$, and denoted $ \operatorname{Res}(f;a)$.



"residue" is owned by djao.
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See Also: Cauchy residue theorem


Attachments:
technique for computing residues (Theorem) by rspuzio
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Cross-references: coefficient, Laurent series, function, domain
There are 26 references to this entry.

This is version 3 of residue, born on 2001-12-28, modified 2006-10-12.
Object id is 1153, canonical name is Residue.
Accessed 6274 times total.

Classification:
AMS MSC: 30D30 (Functions of a complex variable :: Entire and meromorphic functions, and related topics :: Meromorphic functions, general theory)
Pending Errata and Addenda
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