PlanetMath: Mittag-Leffler's theorem

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Mittag-Leffler's theorem

(Theorem)

Let be an open subset of $\mathbb{C}$ , let $\{a_k\}$ be a sequence of distinct points in which has no limit point in . For each , let $A_{1k},\dots,A_{m_kk}$ be arbitrary complex coefficients, and define

$\displaystyle S_k(z) = \sum_{j=1}^{m_k} \frac{A_{jk}}{(z-a_k)^j}.$

Then there exists a meromorphic function

whose poles are exactly the points $\{a_k\}$ and such that the singular part of

, for each

"Mittag-Leffler's theorem" is owned by Koro.

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Cross-references: singular, poles, function, meromorphic, coefficients, complex, limit point, points, sequence, open subset
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This is version 1 of Mittag-Leffler's theorem, born on 2002-12-11.
Object id is 3732, canonical name is MittagLefflersTheorem.
Accessed 4141 times total.

Classification:

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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